this question is for apptitude for cat

1. QA – 1 ] || Ohm Sai Ram || [ Practice Paper
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2. Practice Paper (Solved) ] [ QA – 2
Practice Paper (Solved)
QUANTITATIVE APTITUDE
3 3
1. Three students try to solve a
problem independently with a (a) k = 2 (b) k ≠ 2
probability of solving it as
(c) k ≠ 6 (d) k = 6
1 2 5
, , respectively. What is 5. A bag contains 5 red balls and 8
3 5 12
blue balls. It also contains 4
the probability that the
green and 7 black balls. If a ball
problem is solved ?
is drawn at randomly find the
23 probability that it is not green
7
(a) 30 (b) 5 1
30 6
32 30 (a) (b) 4
(c) 30 (d) 7 1 7
(c) 6 (d) 4
2. From among 36 teachers in a
school one principal and one
vice principal are to be 6. The letters of the word
appointed. In how many ways PROMISE are arranged so that
can this be done ? no two of the vowels should
come together. Find total
(a) 1260 (b) 1250 number of arrangements.
(c) 1240 (d) 1800 (a) 49 (b) 1440
3. A boy has 3 library tickets and (c) 7 (d) 1898
8 books of his interest in the
library. Of these 8, he does not 7. Surendra, Rajendra and
want to borrow chemistry part Manindra invested some
II, unless chemistry part I is amount in a business in the
also borrowed. In how many ratio of 5 :7 : 6 respectively. In
ways can he choose the three the next year they increased
books to be borrowed ? their investments by 26%, 20%
and 15% respectively. The profit
(a) 56 (b) 27 earned during the second year
(c) 26 (d) 41 should be distributed in what
ratio among Surendra,
4. If the system 2x + 3y − 5 = 0, 4x + Rajendra and Manindra
ky − 10 = 0 has an infinite respectively ?
number of solutions, then
(a) 31 : 27 : 21 (b) 21 : 28 : 23

3. QA – 3 ] [ Practice Paper
(c) 26 : 20 : 15 (c) 564 (d) 645
(d) Cannot be determined (e) None of these
(e) None of these 11. Which of the following
expression are exactly equal in
8. Four of the following five parts
value ?
numbered (i), (ii), (iii), (iv) and
(v) are exactly equal. The I. (3x − y)2 − (5x2 − 2xy)
number of the part which is not
II. (2x − y)2
equal to the remaining four is
your answers. III. (2x + y)2 − 2xy
(i) 36 × 15 ÷ 27 × 13 IV. (2x + 3y)2 − 8y(2x + y)
(ii) 53 × 4 × 64 ÷ 16 × 7 (a) I and II only
(iii) 328 ÷ 41 × 21 + 9 × 23 (b) I, II and III only
(c) II and IV only
(iv) 1024 × 11 − 16 × 7
(d) I, II and IV only
(v) 17 × 18 − 121 × 6 (e) None of these
(a) I (b) II 12. Salary of an officer increases
(c) III (d) IV every year by 20%. His salary in
the year 2001 was Rs. 26,640.
(e) V
What was his salary in 1999?
9. A shopkeeper sold an article for
(a) Rs. 20,000 (b) Rs. 19,028
Rs. 6,750 after given a discount
of 10% on the labelled price. He (c) Rs. 18,500 (d) Rs. 18,840
would have earned a profit of (e) None of these
50%, had there been no
discount. What was the actual 13. What approximate value
percentage of profit earned ? should come in place of the
question mark (?) in the
(a) 36 (b) 40 following equation ?
(c) 35 95.9753.5 ÷ 16.0013.5 × 6.0021.5 ÷
(d) Cannot be determined 35.992 = ?
(e) None of these (a) 36 (b) 16
10. From a group of 7 men and 6 (c) 96 (d) 32
women 5 persons are to be (e) 6
selected to form a committee so
that at least 3 men are there on 14. Mr. Anand deposited a total
the committee. In how many amount of Rs. 65,000 in three
different ways can it be done ? different schemes A, B and C
with rates of interest 12 p.c.p.a.,
(a) 756 (b) 735 16 p.c.p.a. and 18 p.c.p.a.

4. Practice Paper (Solved) ] [ QA – 4
respectively and earned a total (a) 81 litres (b) 72 litres
interest of Rs. 10,180 in one
(c) 54 litres (d) 66 litres
year. If the amount invested in
Scheme A was 72% of the 1 1
18. If p + p−
2
amount invested in Scheme 'C', 2 = a, and = b then
p p
what was the amount invested
which of the following is
in Scheme B ?
correctly expressed ?
(a) Rs. 25,000
(a) a − b2 − 2 = 0
(b) Rs. 22,000
(b) a2 + b = 2
(c) Rs. 18,000
(c) a2 − b2 = 1 (d) a2 = b2
(d) Cannot be determined
19. If a + b + c = 0, then the value of
(e) None of these
a(c + a) (a + b) − b(a + b)(b + c) is
15. In how many different ways can equal to :
the letters of the word TRAINER
be arranged so that the vowels (a) 1 (b) a b c
a b
always come together? +
c
(c) (d) 0
(a) 1440 (b) 120
(c) 720 (d) 360 20. A worker earns a 5% raise. A
year later, the worker receives
(e) None of these a 2.5% cut in pay, and now his
16. What will be the value of : salary is Rs. 22702.68. What was
his salary to begin with ?
98 − 72 + 50
(a) Rs. 22000 (b) Rs. 22176
18
38 (c) Rs. 25000 (d) Rs. 22193
(a) 6 (b)
4 3 21. What will come in place of the
(c) − 3 (d) 2 question mark (?) in the
following series ?
17. In a hotel, there are dishonest
waiters. One of them takes out 2 3 10 39 172 ?
one third of the milk from a (a) 704 (b) 885
container full of milk and
replaces it with equal quantity (c) 785 (d) 804
of water. A second waiter again (e) None of these
takes out one third of the
22. A man received a cheque in
mixture and replaces it with
which the rupees were
equal quantity of water. The
transposed for paise and vice
process is repeated by 4 waiters
versa. After spending 5 rupees
resulting in only 16 litres of
42 paise, he discovered that he
milk being left in the container.
now had exactly six times the
What is the capacity of the
value of the correct cheque
container ?

5. QA – 5 ] [ Practice Paper
amount. What amount should 27. Monthly incomes of two
he have received ? persons are in the ratio 5 : 4 and
their monthly expenditures are
(a) Rs. 6.44 (b) Rs. 3.22
in the ratio of 9 : 7. If each
(c) Rs. 18.25 (d) Rs. 8.36 person saves Rs. 500 per month,
23. If α and β are the roots of the then what are their monthly
quadratic equation ax2 + bx + c incomes ?
= 0, then the value of (a) Rs. 8000 and Rs. 10000
2 2
α β (b) Rs. 3750 and Rs. 3000
+ is
β α
3bc a 3abc b (c) Rs. 5000 and Rs. 4000
− 3 − 3 (d) None of these
(a) b c (b) a c
2 2
28. Five persons A, B, C, D and E
3abc b ab b
− 2 − 2c occupy seats in a row such that
(c) a c (d) 2b 2 c A and B sit next to each other.
3
In how many possible ways can
24. 3 chairs and 2 tables cost Rs. these five people sit ?
700, while 5 chairs and 3 tables (a) 24 (b) 48
cost Rs. 1100. What is the cost
of 2 chairs and 2 tables ? (c) 72 (d) None of these
(a) Rs. 300 (b) Rs. 350 29. 26 × 12 ÷ 8 + ? = 76
(c) Rs. 450 (d) Rs. 600 (a) 39 (b) 42
25. If a, b are the two roots of a (c) 43 (d) 37
quadratic equation such that (e) None of these
a + b = 24 and a − b = 8, then the
quadratic equation having a 30. The MSEB electricity bills are
and b as its roots is calculated in the following
manner. The change in meter
(a) x2 + 2x + 8 = 0 reading for the month is
(b) x2 − 4x + 8 = 0 rounded off to the next highest
multiple of 10. The result is
(c) x2 − 24x + 128 = 0 multiplied by 55 paise, and the
(d) 2x2 + 8x + 9 = 0 sum is rounded off to the next
rupee. If the reading last month
26. A sum of money was divided
was 17385 units and this month
among two persons x and y in
it is 18293 units, what is the bill
the ratio 4 : 5. x received Rs. 5
for this month ?
less than y. What is the total
amount of money : (a) Rs. 501 (b) Rs. 495
(a) 45 (b) 50 (c) Rs. 500 (d) Rs. 505
(c) 90 (d) 250 31. A gambler pays Rs. 3 and gets
to throw a dice. He receives an

6. Practice Paper (Solved) ] [ QA – 6
amount equal to the number (c) 100 litres (d) 120 litres
that the top face of the dice
37. There are 10 pairs of socks in a
shows. If the gambler keeps on
drawer. What is the minimum
playing the game, how much
number of socks that a person
does he win per throw, in the
should pull out from the drawer
long run ?
ensure that he gets at least 2
(a) 50 Ps. (b) Rs. 1 matching pairs of socks ?
(c) −50 Ps. (d) Rs. 0 (a) 12 (b) 11
− −
32. |P−10| = 12 & |4J− 10| = 6. What (c) 5 (d) 10
P 38. A painting show drew crowds
is maximum value of . which doubled in number each
J
day. If the show opened on
(a) −11 (b) 22 Monday and the number of
11
spectators on Saturday was
(c) −2 (d) 2 6400, what was the number on
33. If x + y > 5 and x − y > 3, then the opening day?
which of the following gives all (a) 100 (b) 200
possible values of x ?
(c) 800 (d) 80
(a) x > 3 (b) x > 4
39. 15 chairs and 2 tables cost Rs.
(c) x > 5 (d) x < 5 4,000. Find the cost of 12 chairs
34. 136 × 25 ÷ 16 × ? = 2550 and 2 tables, if the cost of 10
chairs be equal to that of 5
(a) 12 (b) 22 tables.
(c) 20 (d) 18 (a) Rs. 4,000 (b) Rs. 4,200
(e) None of these (c) Rs. 3,900 (d) Rs. 3,600
35. The probability of rain on day 40. 5 chairs and 2 tables cost Rs.
1 is 0.2 and the probability on 1,080. The cost of 2 chairs is
day 2 is 0.3. What is the equal to that of a table. Find the
probability of raining on both cost of 2 chairs and 5 tables.
the days?
(a) Rs. 1,440 (b) Rs. 1,480
(a) 0.2 (b) 0.1
(c) Rs. 1,380 (d) Rs. 1,420
(c) 0.06 (d) 0.25
41. An employee spends 30% of his
36. Three − fourths of a tank is full salary on food and donates 3%
of water. If 5 litres are added to of his salary. If he spends Rs.
−
it then four−fifths of the tank 231 on these two items what is
becomes full. What is the his salary ?
capacity of the tank?
(a) Rs. 1250 (b) Rs. 700
(a) 75 litres (b) 80 litres
(c) Rs. 630 (d) Rs. 940

7. QA – 7 ] [ Practice Paper
23 1
42. The mean annual salary paid to
all the staff members of a (c) 30 (d) 2
company was Rs. 5000. The
47. A student on his birthday
mean annual salary paid to
distributed on an average 5
male and female staff were Rs.
chocolates per student. If on the
5200 and Rs. 4500 respectively.
arrival of the teacher and the
Determine the number of male
headmaster to whom the
and female staff members of the
student gives 10 and 15
company.
chocolates respectively, the
(a) 80, 20 (b) 70, 30 average chocolate distributed
(c) 60, 40 (d) 40, 60 per head increases to 5.5, then
what is the strength of the
43. A man has some hens & cows. class?
If the number of heads be 48 and
the number of feet equals 140, (a) 28 (b) 30
the number of hens will be (c) 32 (d) None of these
(a) 26 (b) 24 48. Find the value of
(c) 23 (d) 22 0.2 × 0.2 × 0.2 + 0.02 × 0.02 × 0.02
2 0.4 × 0.4 × 0.4 + 0.04 × 0.04 × 0.04
44. If a b = 5b + a , then (a, b) could
be 0.67 × 0.67 × 0.67 − 0.001
+
0.67 × 0.67 + 0.067 + 0.01
(a) (3, 4) (b) (2, 12)
(a) 4.87 (b) 1.07
(c) (4, 18) (d) (6, 4)
(c) 0.067 (d) 0.002
45. How many bricks are required
to build a wall of 15 metres 49. Find the value of
length, 12 metres height and 20
0.03 × 0.03 + 0.01 × 0.01 - 0.02 × 0.03
cm thickness, if the brick is 36
cm long, 25 cm wide and 10 cm 0.02
thick ? FG 3 + 1 of 3 IJ
(a) 2000 (b) 4000
÷
H 8 2 16K
(c) 12000 (d) None of these (a) 0.447 (b) 8.04
46. Three students try to solve a (c) 0.0427 (d) 0.012
problem independently with a
probability of solving it as 0.289 24 + 216
50. Simplify : +
2 4 3 0.00121 96
, , respectively. What is
8 5 4 (a) 12.45 (b) 16.54
the probability that the
problem is solved ? (c) 18.90 (d) 17.45
12
3 51. A pack of 52 cards is distributed
(a) (b) 30 amongst 4 players. The one to
20

8. Practice Paper (Solved) ] [ QA – 8
receive the set with the lowest (c) 9 (d) 12
sum wins
56. If x1/3 + y1/3 + z1/3 = 0, then :
(A = 1, J = 11, Q = 12, K = 13).
(a) x + y + z = 0
What is the least total with
(b) (x + y + z)3 = 27 xyz
which one can win ?
(c) x + y + z = 3 xyz
(a) 40 (b) 31
(d) x3 + y3 + z3 = 0
(c) 28 (d) 24
57. A crown, made of gold, silver,
52. If every 2 out of 3 readymade
copper and brass weighs 9.725
shirts need alterations in the
kg. The weight of the gold and
collar, every 3 out of 4 need
silver together is 4 kg and the
alterations in the sleeves, and
weight of the gold and copper
every 4 out of 5 need it in the
4.5 kg and of the gold and brass
body, how many alterations
3.6 kg. What is the weight of
will be required for 60 shirts ?
gold in the crown ?
(a) 123 (b) 133
(a) 1.2500 kg (b) 2.6575 kg
(c) 143 (d) 24
(c) 1.1875 kg (d) 2.3705 kg
53. Which of the following does not
58. A bag contains 3 white balls
belong to the group ?
and 2 black balls. Another bag
10 , 11 , 18, 36, 74 contains 2 white balls and 4
black balls. A bag and a ball are
(a) 10 (b) 11
picked at random. The
(c) 18 (d) 36 probability that the ball will be
54. Tulsi had a children's party and white is
bought two mangoes for each 7 7
child. However, a quarter of the (a) 11 (b) 30
kids invited did not come. 25
boys came and the surplus 5 7
provided just one extra mango (c) 11 (d) 15
for each girl. How many
mangoes did Tulsi buy ? 59. One hundred identical coins
(a) 200 (b) 132 each with probability p of
showing up heads are tossed. If
(c) 150 (d) 128 0 < p < 1 and the probability of
−
55. If x is a three−digit number and heads showing on 50 coins is
y is a number obtained by equal to that of heads on 51
permuting the digits of x in any coins, then the value of p is
manner, then (x − y) is always 1 49
divisible by : (a) 2 (b) 101
(a) 4 (b) 6

9. QA – 9 ] [ Practice Paper
50 51 65. With the same data as for the
(c) 101 (d) 101 previous question, what is the
probability that the next
60. Two dice are tossed. The program will run correctly
probability that the total score after the third run, but not
is a prime number is earlier ?
9 3
1 5
(a) 10 (b) 10
(a) 6 (b) 12
7 1
1 7 (c) 20 (d) 10
(c) 2 (d) 9
66. A number is greater than the
FG 1 IJ −2 square of 44 but smaller than
61. The value of
H 4K 1
is the square of 45. If one part of
the number is the square of 6
and the number is the multiple
(a) 2 (b) − 2
of 5, then find the number.
1
(a) 1940 (b) 2080
(c) − 16 (d) 16
(c) 1980
62. The volume of a cube is V. The
total length of its edges is (d) Cannot be determined
(e) None of these
(a) 6 V1/3 (b) 8 V
67. Rajesh solved 80 per cent of the
(c) 12 V2/3 (d) 12 V1/3 questions in an examination. If
63. A boy was asked to write 25 × out of 41 questions solved by
9 2 , but he wrote 2592. The Rajesh 37 questions are correct
numerical difference between and of the remaining questions
the two is out of 8 questions 5 questions
have been solved by Rajesh
(a) 0 (b) 1 correctly then find the total
(c) 2 (d) 3 number of questions asked in
the examination ?
x 2 − 36 x+6
64. If P = and Q = , then (a) 75 (b) 65
x − 49
2
x+7
P (c) 60
the value of is
Q (d) Cannot be determined
x 6 x 6
−7 − (e) None of these
(a) x (b) x 7
− + 68. What was the day on April 6,
x 2001?
(c) x −76 x+6
(a) Friday (b) Saturday
+ (d) x − 7
(c) Thursday (d) Sunday

10. Practice Paper (Solved) ] [ QA – 10
69. Monthly incomes of two 74. 76.59 + 129.052 − 38.314 = ? +
persons are in the ratio 5 : 4 and 45.72
their monthly expenditures are
in the ratio of 9 : 7. If each (a) 121.068 (b) 121.608
person saves Rs. 500 per month, (c) 120.068 (d) 120.608
then what are their monthly
incomes ? (e) None of these
(a) Rs. 8000 and Rs. 10000 75. 336 ÷ 12 × 15 − ? = 138
(b) Rs. 3750 and Rs. 3000 (a) 140 (b) 233
(c) Rs. 5000 and Rs. 4000 (c) 420 (d) 282
(d) None of these
(d) None of these
76. 168 × 15 ÷ 24 × 12 = ?
70. Income of C is 20% more than
that of B and income of B is 25% (a) 1160 (b) 8.75
more than that of A. Find out (c) 1260 (d) 105
by how much % is the income
of C more than that of A. (e) None of these
(a) 25% (b) 75% 77. 4410 ÷ 45 ÷ 7 = ?
(c) 50% (d)100% (a) 98 (b) 686
71. Spending Rs. 1,200 daily for 7 (c) 14 (d) 70
days, I ran into a debt which (e) None of these
was cleared in 9 days after I
reduced my daily expense to Rs. 78. 7586 + 11254 − ? = 8976
880. Find my daily income. (a) 9846 (b) 9764
(a) Rs. 1,000 (b) Rs. 1,020 (c) 9784 (d) 9864
(c) Rs. 1,040 (d) Rs. 1,025 (e) None of these
72. The ratio of incomes of A and B 79. 1111 + 12121 + 1020102 = ?
is 5 : 3 and that their
expenditures is 8 : 5. If their (a) 1303334 (b) 1033344
savings are in the ratio of 2 : 1 (c) 103334 (d) 1033334
and their total saving is Rs.
3,600, then the income of A is : (e) None of these
(a) Rs. 12,000 (b) Rs. 7,200 80. There are two grades A and B
of workers in a workshop.
(c) Rs. 7,800 (d) Rs. 9,100 Every worker contributes as
many rupees as there are
73. 1.5 × 1.2 − 0.06 × 0.5 = ? workers of his own category. If
(a) 1.77 (b) 17.97 the total amount contributed is
(c) 1.797 (d) 17.77 Rs. 196 including Rs. 16
contributed by the owner of the
(e) None of these workshop, what is the total

11. QA – 11 ] [ Practice Paper
number of workers in that 88. A person wants to divide a sum
workshop ? of Rs. 3,90,300 between his two
sons who are 13 and 15 years of
(a) 18 (b) 14 (c) 12
age respectively in such a way
(d) 10 (e) None of these that their shares, if invested at
4% per annum compound
196 17 78
81. × × =? interest, should produce the
14 289 169 same amount when they
(a) 1 (b) 2 (c) 6 become 18 years of age. Find the
(d) 4 (e) 13 share of each.
? (a) 187500, 202800
82. = 250
.25 (b) 178500, 183000
(a) 500 (b) 125 (c) 5 (c) 199400, 194500
(d) 0 (e) 100 (d) 168390, 195600
189 89. A, B and C invested Rs. 26,000,
83. = 1.89 Rs. 34,000 and Rs. 10,000
a
respectively in a business.
(a) 10 (b) 100 (c) 1000 They earn a profit of Rs. 3500.
(d) 10000 (e) None of these B's share of profit is
(a) Rs. 1200 (b) Rs. 1500
84. 12 + 24 equals
(c) Rs. 1700 (d) Rs. 1900
(a) 2 6 + 2 3 (b) 36
90. Mr. Rai decided to distribute his
(c) 288 (d) 6 2 income among the members of
85. Find 100 + 49 his family. He gave 50% to his
wife, 35% of the remaining to
(a) 149 (b) 17 (c) 490 both of his sons, and the
(d) balance of Rs. 6,750 was
14 + 10 (e) None of these
deposited by him in the bank.
86. 0.00004761 equals How much amount was received
by his wife ?
(a) 0.069 (b) 0.0069
(a) Rs. 23,200 (b) Rs. 45,000
(c) 0.00069 (d) 0.0609
(c) Rs. 22,500 (d) Rs. 13,500
3
87. If x = , find the value of (e) None of these
2
91. If a ⊗ b = (a × b) + b, then 5 ⊗ 7
1 + x+ 1 - x
equals to
1 + x− 1 - x
(a) 12 (b) 35
(a) 5 (b) 3 (c) 42 (d) 50
(c) 2 (d) 4 92. 24% of 250 + ?% of 240 = 120

12. Practice Paper (Solved) ] [ QA – 12
(a) 25 (b) 40 98. (1502)2 − (1498)2 = ?
(c) 30 (d) 45 (a) 12,000 (b) 16,000
(e) None of these (c) 22,56,004 (d) 22,560
93. 22% of ? + 30% of 420 = 192 3
99. of 480 ÷ 8 + 82 = ?
(a) 330 (b) 350 5
(a) 120 (b) 100
(c) 200 (d) 280
(c) 36 (d) 44
(e) None of these
100. Value of 64 ÷ 8 ÷ 4 ÷ 2 is
94. 75 × 18 + ?% of 150 = 1380
(a) 1 (b) 8
(a) 25 (b) 20
(c) 16 (d) 24
(c) 12 (d) 16
(e) None of these
(e) None of these
101. If a : b = 2 : 3, b : c = 5 : 7, then a
95. Subhash bought 20 kg of tea at : b : c is
the rate of Rs. 30 per kg and 30
kg at the rate of Rs. 25 per kg. (a) 2 : 3 : 7 (b) 2 : 5 : 7
He mixed the two and sold the (c) 10 : 15 : 21 (d) 2 : 15 : 7
mixture at the rate of Rs. 22.50
per kg. What was his loss in the (e) None of these
transaction ? 102. If two numbers are in the ratio
(a) Rs. 200 (b) Rs. 225 5 : 7and their least common
multiple is 315, then their
(c) Rs. 175 (d) Rs. 200.25 product is
96. A boy goes to school with the (a) 2385 (b) 2538
speed of 3 km/hr and returns
with a speed of 2 km/hr. If he (c) 2358 (d) 2835
takes 5 hours in all, the distance 103. If x : y = 3 : 4, y : z = 5 : 6 and z : w
in kms between the village and = 2 : 3, then x : w equals
the school is
(a) 5 : 3 (b) 3 : 3
(a) 6 (b) 7
(c) 5 : 12 (d) 7 : 3
(c) 8 (d) 9
104. Subtract − 13 from 28 − 5 + 5.
97. Gold is 19 times heavy as water
(a) 51 (b) 53
and copper 9 times as heavy as
water. The ratio in which these (c) 56 (d) 58
two metals be mixed so that the
(e) None of these
mixed so that the mixture is 15
times as heavy as water, is 105. Add 7.007, 70.7 and 7.007
(a) 1 : 2 (b) 2 : 3 (a) 84.074 (b) 84.714
(c) 3 : 2 (d) 19 : 135 (c) 84.741 (d) 80.714

13. QA – 13 ] [ Practice Paper
106. Which of the following 2 1
112. Express of of Rs. 25.20 as a
numbers is a multiple of 8 ? 3 4
(a) 923862 (b) 923962 1
fraction of 1 of Rs. 36.
2
(c) 923972 (d) 923872
7 11
107. If 14% of a number is 105, then (a) (b)
90 90
find the number.
5 5
(a) 715 (b) 705 (c) (d)
8 42
(c) 735 (d) 750
113. Simplify :
LM R F I UOP
108. Three pipes fill a tank
separately in 10 minutes, 20
1+ 2 3− 1+ 2−
| G
S H 1 5
− JK |PQ
V
minutes and 30 minutes
respectively. An outlet pipe can
MN |
T 2 2 |
W
empty it in 15 minutes when no (a) 2 (b) 1
water flows in. If all the pipes (c) −3 (d) 5
are opened, when the tank is
empty, then how long, in 114. The least of the following
minutes, will it take to fill the
tank ?
2
b g
0.2, .2 , 0.2 , 1 ÷ 0.2 is
1 4 (a) (.2)2 (b) 0.2
(a) 9 (b) 8
7 7 (c) 0.2 (d) 1 ÷ 0.2
1 2
(c) 7 (d) 6 115. 5% of 5% of Rs. 100 is
2 3
109. A number is multiplied by its (a) Re. 0.25 (b) Re. 0.50
−
one−third to get 192. Find the (c) Rs. 10 (d) Rs. 25
number.
116. The value of
(a) 16 (b) 20
(c) 24 (d) 28 6 + 6 + 6 + 6+.... is
110. The value of
(a) 2 (b) 5
0.125 + 0.027
is (c) 4 (d) 3
0.5 × 0.5 + 0.09 − 0.15
117. A cistern is normally filled with
(a) 1 (b) 0.2
water in 10 hours but takes 5
(c) 0.08 (d) 0.8 hours longer to fill because of
a leak in its bottom. If the
0.01 + 0.0064 cistern is full, then the leak will
111. Evaluate :
0.01 × 0.3 empty the cistern in
(a) 1 (b) 10 (a) 20 hours (b) 40 hours
(c) 100 (d) 1000 (c) 50 hours (d) 30 hours

14. Practice Paper (Solved) ] [ QA – 14
118. Taps A and B can fill a bucket
in 12 minutes and 15 minutes b12.12g − b8.12g 2 2
respectively. If both are opened
and A is closed after 3 minutes,
120. Simplify
b0.25g + b0.25gb19.99g
2
how much further time would LMe8 j OP × 16
-3/4
5/2
8/15
3/4
+N Q
it take for B to fill the bucket ?
(a) 8 min 5 sec. (b) 8 min 15 sec.
LMF b128g I OP 3/7
−1/5
NH K Q
-5
3
(c) 7 min 45 sec. (d) 7 min 15 sec.
119. A and B enter into a
1 1
partnership investing Rs. (a) 4 (b) 6
12,000 and Rs. 16,000 2 2
respectively. After 8 months, C 2 1
also joins the business with a (c) 3 (d) 8
3 2
capital of Rs. 15,000. The share
121. Find the value of
of C in a profit of Rs. 45,600 after
1 1
e28 + 10 3 j − e7 − 4 3 j
two years is
2 2
(a) Rs. 12,000 (b) Rs. 14,400
(a) 5 (b) 3
(c) Rs. 19,200 (d) Rs. 21,200
(c) 8 (d) 6
(e) None of these
ANSWERS & SOLUTIONS
Ans.1.(a) Let three students are A, B and Ans.3.(c) There are two ways of
C ⇒ Probability that the given problem borrowing books
cannot be solved by A, B & C is (a) When there is no chemistry book in
1 2 5 2 3 7 7
FG
1 IJ FG
1 1IJ FG IJ this case, 3 books are to be selected from
H −3
KH
−5
KH K
− 12 = 3 × 5 × 12 = 30 the remaining 6 books :
⇒ Probability that the problem is solved This can be done in = 6C3
7
FG IJ
30 = 23
6 5 4
× ×
=1−
H K30
= 1 2 3 = 20 ways
× ×
Ans.2.(a) One principal can be (b) When there is a chemistry 1 and
appointed out of 36 teachers = 36C1, 36 chemistry 11 books. In this case one
ways. book can be selected from the remaining
For each way of doing so, one vice 6 books in = 6C1 = 6 ways. Hence, total
number of ways = 20 + 6 = 26
principal can be appointed out of the
remaining 35 teachers in 35C1 = 35 ways Ans.4.(d) The equation is same only if
k=6
Hence, two posts, together can be filled
(by multiplying the first equation by 2).
in 36 × 35 = 1260 ways.

15. QA – 15 ] [ Practice Paper
Ans.5.(a) Probability of not given Ans.13.(e) Given expression
5 8 7 20 5
+ + 96 3 × 96 6× 6
5 8 7 4 = 24 = 6 = ×
3
+ + + 16 × 16 64
Ans.6.(b) 7! = (3C2 × 6! × 2! + 5!) simplyfying the expression,
= 5040 − (3 × 720 × 2 + 120) = 1440. we get its value as 6.
Ans.7.(b) In the second year the Ans.14.(b) If C = 100, A = 72.
investment are : Hence ratio = 25 : 18.
5 × 1.26 : 7 × 1.20 : 6 × 1.15 Then 18x + 25x + y = 65,000 and 12%
= 6.3 : 8.4 : 6.9 = 21 : 28 : 23. (18x) + 18% (25x) + 16% (y) = 10, 180.
15
Solving the two equations,
Ans.8.(a) 36 × 27 × 13 = 260.
we get y = 22,000.
All other parts equal 240.
Ans.15.(c) Country the vowels as one,
100
Ans.9.(c) MP = 6750 × 100 we have 5! ways.
90 = 7500.
Since the vowels can be arranged in 3!
× 150 .
Since profit1750
= 50%, C.P. = 7500 ways, the reqd. answer is 5! × 3! = 720.
Profit % = 5000 × 100 = 35%. Ans.16.(d) Reduce to the base of 2 by
Ans.10.(a) Since there are at least 3 factorisation and solve.
men in the committee, we can have 3 Ans.17.(a) Milk left after 4th operation/
cases, either 3 or 4 or 5 men. Whole quantity of container
1 4 16
(i) 7C3 × 6C3 (ii) 7C4 × 6C1 1 FG IJ
(iii) 7C
5 × 6C
0 = 525 + 210 + 21 = 756
=
H
−3 =
x K ⇒ x = 81 litres.
Ans.11.(c)
p 1 2 FG IJ 1
− p = P 2 + 2 − 2.
I. 9x2 + y2 + 6xy − 5x2 + 2xy
Ans.18.(a)
H K P
= 4x2 + y2 + 8xy Hence b2 = a − 2.
II. (2x − y)2 = 4x2 + y2 − 4xy Ans.19.(d)
III. 4x2 + y2 + 4xy − 2xy a(c + a)(a + b) − b (a +b)(b + c)
= 4x2 + y2 + 2xy = abc − abc = 0.
IV. 4x2 + 9y2 + 12xy − 16xy − 8y2 Ans.20.(b) Suppose the salary was Rs.
100, to begin with.
3= 4x2 + y2 − 4xy
⇒ 100 + 5% = 105
Hence only II and IV are equal. ⇒ 105 − 2.5% = 102.375
Ans.12.(c) Salary 2 years back If the present salary is Rs. 102.375, then
100 100 the salary in the beginning was Rs. 100.
= 26,640 × ×
120 120 = 18,500.

16. Practice Paper (Solved) ] [ QA – 16
If the present salary Rs. 22702.68, then Ans. 25.(c) a + b = 24, a − b = 8
the salary the beginning was
100 ⇒ a = 16, b = 8 ⇒ ab = 128
102.375 × 22702.68 = 22176. ⇒ Required equation is the one whose
sum of the roots is 24 and product of the
Ans.21.(b) The sequence in the given
roots is 128.
series is
i.e. x2 − 24 x + 128 = 0
× 1 + 12, × 2 + 22, × 3 + 32, × 4 + 42, x
× 5 + 52. y =4
Ans.26.(a) 5,x=y−5
Ans.22.(a) The cheque was received for 4y 4y
Rs. 44.06. After spending Rs. 5.42, he
⇒ x= 5 , 5 =y−5
had Rs. 38.64, which is 6 times of Rs.
6.44. ⇒ y = 25, x = 20 ⇒ x + y = 45
∴ He should have received Rs. 6.44. = Total amount
c
b
Ans.23.(b) α + β = − αβ = a Ans.27.(c) Let the monthly incomes of
a, two persons be 5I and 4I and their
α2 + β2 = (α + β)2 − 2αβ monthly expenditures be 9E and 7E
b c b ac respectively.
2 2
2 −2
= a − a = a
2 2 ⇒ 5I − 9E = 500
α 2 β2 α 3 + β 3 ⇒ 4I − 7E = 500
⇒ + =
β α αβ ⇒ I = 1000, E = 500
(α + β)(α 2 + β2 − αβ) ⇒ Monthly incomes of the two persons
= are Rs. 5000 and Rs. 4000.
αβ
FG − b IJ FG b 2
− 2ac c I
JK Ans.28.(b) 4! × 2 ways,
=
H aKH a2
−
a i.e. 24 × 2 = 48 ways.
c
Ans.29.(d) 26 × 12 ÷ 8 + ? = 76
a
2 3 12
− b (b − 3 a c) a abc − b 3 ⇒ 26 × + ? = 76
3 × = 8
a c a 2c
⇒ ? = 76 − 39 = 37
Ans.24.(d) 3C +2T = 700 Ans.30.(a) Change in meter reading
5C + 3T = 1100 = 18293 − 17385 = 908 units.
⇒ 9C + 6T = 2100 Rounded off to 910 units.
⇒ 10C + 6T = 2200 Therefore Bill is (910)(55) = 50050 paise,
⇒ C = 100, T = 200 or Rs. 500.50.
⇒ 2C + 2T = 200 + 400 = 600. This is rounded off to Rs. 501.

17. QA – 17 ] [ Practice Paper
10
Ans.31.(a) In the long run, every
number will have occurred roughly the Ans.37.(c) x (5) 2 = 5
same number of times.
Ans.38.(b) Let the no. of crowds on the
Therefore for every 6 throws, each opening day = x
number from 1 to 6 would have occurred.
Monday = x, Tuesday = 2x
Therefore the gambler would have won
1 + 2 + 3 + 4 + 5 + 6 i.e. Rs. 21. Wednesday = 4x, Thursday = 8x
He would have spent Rs. (6 × 3) = 18. Friday = 16x,
Therefore gain is Rs. 3 in 6 throws,
Saturday = 32x = 6400
i.e. 50 paise per throw. 6400
P
⇒ x = 32 = 200.
Ans.32.(b) J max ⇒ P max, J min
Ans.39.(c) Let cost of a chair and a table
[P − 10] = 12 ⇒ P = 22 or − 2 be Rs. x and y respectively.
[4J − 10] = 6 ⇒ J = 4 or 1. Then, 15x + 2y = 4000 .....(i)
P
10x = 4y ....(ii)
So max. value of J is 22.
Solving (i) and (ii)
Ans.33.(b) x + y > 5 x = 200, y = 500
x − y > 3, 2x > 8, x > 4. 12x + 3y = 12 × 200 + 3 × 500
Ans.34.(a) 136 × 25 ÷ 16 × ? = 2550 = Rs. 3900
25 Ans.40.(a) 5x + 2y = 1080 .....(i)
⇒ 136 × × ? = 2550
16 2x = y or 2x − y = 0 ......(ii)
2550 × 16 Solving (i) and (ii),
⇒ ? = 136 25 = 12
×
x = 120, y = 240.
Ans.35.(c) P(A) = 0.2, P(B) = 0.3
⇒ 2x + 5y = 2 × 120 + 5 × 240
P(A ∩ B) = P(A).P(B)
= Rs. 1440.
= 0.2 × 0.3 = 0.06
Ans.41.(b) Let his salary = Rs. x
Ans.36.(c)
Expenditure on food
Let the capacity of tank = x liter. 30 3x
3 4 3x 4 x =x × 100 = Rs. 10
4 x + 5 = 5 x ⇒ 4 − 5 = −5
3 3x
x
15x 16x Donation = × 100 = 100
−
20 −x
= −5 ⇒ −5 3x 3x
20 =
⇒ 10 + 100 = 231
⇒ x = 100

18. Practice Paper (Solved) ] [ QA – 18
30x 3 x 1 4 3 12 3
100+ 4 × 5 × 4 = 80 = 20
⇒ = 231 Ans.46.(a)
33 x
Ans.47.(a) Suppose strength of the class
⇒ 100 = 231
= x ⇒ 5x + 10 + 15 = 5.5(x + 2)
⇒ 33x = 231 × 100
100 ⇒ 0.5x = 14 ⇒ x = 28
⇒ x = 231 × 33 = 700. Ans.48.(b) Given expression
1 (0.67) 3 − (0.1) 3
Ans.42.(b) Let the of ratio of male and = +
female is K : 1 2 (0.67) 2 + 0.67 × 0.1 + (0.1) 2
1
⇒ 5200 K + 4500 = (K + 1) × 5000 = 2 + (0.67 − 0.1)
⇒ 5200 K + 4500 = 5000K + 5000 [ ... a3 − b3 = (a − b)(a2 + b2 + ab)]
⇒ 5200 K − 5000K = 5000 − 4500 = 500 = 0.5 + 0.57 = 1.07
500 5
Ans.49.(c) Given expression
200 K = 500 ⇒ K = 200 = 2 (0.03) 0.01 2 2 0.01 0.03
5
=
2
+ b g
− ×
0.02
×
K:1= 2 :1=5:2 FG 3 + 3 IJ
= 70 : 30 = 70, 30
÷
H 8 32 K
Ans.43.(a) Let No. of hens = x (0.03 − 0.01) 2 32 0.02 × 32
× =
⇒ No. of cows = (48 − x) = 0.02 15 15
⇒ 2x + 4 (48 − x) = 140 0.64 64 16
= = = 0.0427
15 1500 375 =
⇒ 2x + 192 − 4x = 140
Ans.50.(d) Given expression
⇒ −2x = 140 − 192 = −52
52 28900000 24 + 24 × 9
= +
⇒ x = 2 = 26 121000 96
Ans.44.(b) Put a = 2, b = 12 in 170 4 24 170 192
= + = +2= = 17.45
a 11 2 24 11 11
b = 5b + a2
Ans.51.(c) Required number
2
⇒ 12 = 5 × 12 + 4 = 64 = (4 × 1) + (4 × 2) + (4 × 3) + (1 × 4)
⇒ 26 = 64, which is true. = 4 + 8 + 12 + 4 = 28.
Ans.45.(b) No. of bricks required Ans.52.(b) Total number of alteration
1500 1200 20 for 60 shirts
2 3 4
= 36 × 25 70
×
= 4000
× × = [ 3 × 60 + 4 × 60 + 5 × 60] = 133.

19. QA – 19 ] [ Practice Paper
Ans.53.(d) 10 = 10 + 03 i.e. G + S + C + B = 9.725 ......(i)
⇒ 11 = 10 + 13 ⇒ 18 = 10 + 23 where G = part of gold in crown
S = part of silver in crown
⇒ 36 = 10 + ?3
C = part of copper in crown
⇒ 74 = 10 + 43
B = part of brass in crown
The number in the series at position 4
must be 10 + 33 = 37. Again by the condition of the question :
Therefore the number 36 does not G + S = 4 kg .......(ii)
belong to the group. G + C = 4.5 kg .......(iii)
Ans.54.(a) Let number of children = x. G + B = 3.6 kg .......(iv)
So number of mangoes purchased = 2x.
add (ii) + (iii) + (iv)
Number of children present
x 3x 3G + S + C + B = 12.1 kg
=x− 4 = 4 . 2G + 9.725 = 12.1 ⇒ 2G = 2.375
3x
Number of girls = 4 − 25. ⇒ G = 1.1875 kg.
Now by the question, Ans.58.(d) Prob. that bag A is drawn =
1
FG 3x − 25IJ × 3 + a25 × 2f = 2x 2 . Prob. that white ball is drawn from
1
H4 K bag A = 2 × =
3
5 10
3
⇒ x = 100. So the number of mangoes 1
purchased = 200. Prob. that bag B is drawn = 2
Ans.55.(c) Suppose the hundred's, ten's Prob. that white ball is drawn from bag
and unit's places of x be a, b, c 1 2 1
× = .
respectively. Make these digits as c, b, a. B= 2 6 6
Difference of numbers Prob. that white ball is drawn either
= (100a + 10b + c) − (100c + 10b + a) from bag A or from bag B
= 99 (a − c), which is divisible by 9 but 3 1 7
= + =
none of 4, 6, 12. 10 6 15
Ans.56.(b) Using a + b + c = 0 Ans.59.(a) P50 (1 − p)50 = P51 (1−P)49
1
⇒ a3 + b3 + c3 = 3abc, ⇒ P=
2
we get, x1/3 + y1/3 + z1/3 = 0
Ans.60.(b) Total score will be a prime
⇒ x + y + z = 3x1/3 y1/3 z1/3 number in 15 ways out of 36 :
⇒ (x + y + z)3 = 27 xyz. (1,1), (1,2), (1,4), (1,6), (2,1),
Ans.57.(c) Given that the crown made (2,3), (2,5), (3,2), (3,4), (4,1),
of gold, silver, copper and brass and (4,3), (5,2), (5,6), (6,1), (6,5).
weighs 9.725 kg,

20. Practice Paper (Solved) ] [ QA – 20
4
Hence, the required probability
= 80% of n = 5 n
15 5
= =
36 12 Now, according to the question,
FG 1 IJ −2
FG 4 IJ 2 5 4n
Ans.61.(d)
H 4K =
H 1K = 16 37 + (n − 4) ×
5n
8 = 5
205 4n
Ans.62.(d) There are 12 edges in the
cube, Volume = V. or, 37 + 8 − 8 = 5
205 4n 5n
Each edge = V1/3.
or, 37 − 8 = 5 − 8
Total length of the edges = 12 V1/3.
296 205 32 25
Ans.63.(a) 25 × 92 = 32 × 81 = 2592 −
8 −
n40 n
or, =
P x 2 − 36 x + 7 x−6
Ans.64.(a) = 2 × = .
Q x − 49 x + 6 x −7 91 7n
2 7 5 =
1 FG
20 + 20 + 20 = 3 IJ or 8 91 40
40
Ans.65.(b) − H 10 K ×
⇒ n = 8 7 = 65
×
Ans.66.(c) Let the number be N
Therefore, total number of questions =
⇒ According to the question, 65. Thus the required answer is
option (b).
(44)2 < N < (45)2 ⇒ 1935 < N < 2025
Ans.68.(a) Complete years 2000. No. of
Therefore, the required number would odd−days in 2000 = 0.
be any number between 1937 and 2025.
Odd day in Jan = 3, Feb = 0, March = 3,
But from the question it is clear that the April 6, Total = 12, and odd days = 5.
required number is the factor of 6 and Day = Sunday + 5 = Friday
the multiple of 5. So we have to find out
the number between 1937 and 2025 Ans.69.(c) Let x denote the monthly
which is divisible by both 36 and 5. income variable and y denote the
monthly expenditure.
62 = 36
As per question,
LCM of 36 and 5 = 36 × 5 = 180
5 9
180 × 10 = 1800 x− y = 500 .................(i)
9 16
180 × 11 = 1980
4 7
Thus the required no. is 1980. and x− y = 500 .........(ii)
9 16
So, Answer is (c). Solving (i) and (ii) x = 900
5
Ans.67.(b) Let the total number of
questions asked in examination be n. ⇒ Their monthly income are 9 x and
4
⇒ No. of correct answer 9 x = Rs. 5000 and Rs. 4000
respectively.

21. QA – 21 ] [ Practice Paper
Ans.70.(c) C = B + 20% of B
B 6B ⇒ 13232 + 1020102 = ?
=B+ 5 = 5 . ⇒ ? = 1033334
A 5A
Ans.80.(a) The contribution by the
B = A + 25% of A = A + 4 = 4 workers in the workshop = 196 − 16 =
6 6 5 3 Rs. 180. Let the number of workers in A
⇒ C= 5B= 5×4 A= 2 A grade be x and in B grade be y.
A ∴x2 + y2 = 180.
= A + 2 = A + 50% of A Now, by putting x = 12 and y = 6,
Ans.71.(b) Let my daily income be Rs. we get x2 + y2 = 180
x.
∴x + y = 12 + 6 = 18
Then, 7 (1200 − x) = 9 (x − 880) x = 1020.
196 17 78
Ans.72.(a) Ans.81.(c) × × =?
14 289 169
Saving of A = 2400, of B 1200.
14 × 14 17 78
Then, 5x − 8y = 2400 and 3x − 5y = 1200. ⇒ ?= × ×
14 17 × 17 13 × 13
Solving, we get x = 2400.
Hence 5x = 12,000. 14 17 78 18564
⇒ ? = 14 × 17 × 13 = 3094 = 6
Ans.73.(a) ? = 1.5 × 1.2 − 0.06 × 0.5
?
= 1.80 − 0.030 = 1.770 = 1.77 Ans.82.(b) = 250
0.25
Ans.74.(b)
⇒ ? = 250 × 0.25
76.59 + 129.052 − 38.314 = ? + 45.72
⇒ 250 × 0.5 × 0.5 = 250 × 0.5
⇒ 205.642 − 38.314 − 45.72 = ?
5
⇒ 167.328 − 45.72 = ? ⇒ ? = 121.608 ⇒ 250 × = 125
10
Ans.75.(d) 336 ÷ 12 × 15 − ? = 138 Ans.83.(d)
189
= 1.89 ⇒
189
= a
a 1.89
⇒ ? = 336/12 × 15 − 138
18900
= 28 × 15 − 138 = 420 − 138 = 282 ⇒ = a , Squaring both sides
189
15
Ans.76.(c) ? = 168 × × 12 = 1260 (100)2 = ( a )2 ⇒ 10000 = a
24
Ans.77.(c) 4410 ÷ 45 ÷ 7 = 98 ÷ 7 = 14 Ans.84.(a) 12 + 24
Ans.78.(d) 7586 + 11254 − ? = 8976 = 2×2×3 + 2×2×2×3 = 2 3+2 6
⇒ 18840 − 8976 = ? Ans.85.(b) 100 + 49
⇒ ? = 9864 ⇒ 10 × 10 + 7 × 7 = 10 + 7= 17
Ans.79.(d) 1111 + 12121 + 1020102 = ?

22. Practice Paper (Solved) ] [ QA – 22
Ans.86.(b) 0.00004761 FG 4 IJ 5
b g FGH1 + 100 IJK
4
3
4761 69 × 69
H
x 1+
10 0 K = 390300 − x
= =
100000000 10000 × 10000 676
x = (390300 − x)
69 625
= = 0.0069
10000
⇒ x = 187500 and y = 390300 − 187500
Ans.87.(b)
⇒ y = 202800
1 + x + 1− x 1 + x + 1− x
× Ans.89.(c) Profit of Rs. 3500 is divided
1 + x − 1−x 1 + x + 1− x among A, B and C in the ratio 26000 :
=
e 1 + x + 1− x j 2 34000 : 10000.
i.e. in the ratio 13 : 17 : 5.
e 1 + x j e
2
− 1− x j 2
∴B's share of profit =
17
× 3500
35
1 + x + 1 − x + 2 1 − x2 1 + 1 − x2
=
a
1 + x − 1− xfa f =
x
= Rs. 1700.
Ans.90.(c) 15% of the income = Rs. 6750
1 + 1 − 34 1+ 1 ∴ Total income = Rs. 45000
= = 2= 3
3
3 ⇒ Amount given to the wife by Mr. Rai
2 2
= Rs. 22500
Ans.88.(a) Let x and y be the shares of
the two sons. Ans.91.(c) 5 ⊗ 7 = (5 × 7) + 7 = 42
∴x + y = 3,90,300 24 ?
Ans.92.(a) × 250 +
× 240 = 120
⇒ y = (390300 − x) 100 100
For the boy of age 13 years, ? × 12
⇒ 60 + = 120
= 5 years, Rate = 4%, Principal = x 5
∴Amount after 5 years compounded
⇒? =
b
120 − 60 × 5
= 25
g
FG 4 IJ 5 12
annually
H
= x 1+
100 K .......(i)
Ans.93.(e)
22
100
×?+
30
100
× 420 = 192
For the boy of age 15 years :
22 × ?
Time = 3 years, Principal = 390300 − x ⇒ = 192 −126 = 66
100
∴Amount after 3 years compounded
annually
⇒ ? = 300
Ans.94.(b) ? % of 150 + 75 × 18 = 1380
b g FGH1 + 100 IJK
3
4
= 390300 − x ......(ii) ?
⇒ × 150 + 1350 = 1380
100
From (i) & (ii), we get 3000
⇒? = ⇒ ? = 20
150

23. QA – 23 ] [ Practice Paper
Ans.95.(b) C.P. of 50 kg. of tea ⇒ 35 K = 315 ⇒ K = 9
= Rs. (20 × 30 + 30 × 25) = Rs. 1350. Hence the numbers are 45 and 63.
S.P. of 50 kg. of tea = Rs. (50 × 22.50) Their product is 2835.
= Rs. 1125. X 3 Y 5 Z 2
Ans.103.(c) = , = , =
Y 4 Z 6 W 3
Loss = Rs. (1350 −1125) = Rs. 225.
X Y Z W
⇒ = = =
2×3×2 2d 15 20 24 36
Ans.96.(a) =
3+2 5 ⇒ X : W = 15 : 36 = 5 : 12
LM Average Speed 2xy OP Ans.104.(e) 28 − 5 + 5 − (−13) = 41
N =
x+y Q Ans.105.(b) 7.007 + 70.7 + 7.007 =
∴10 d = 60 or d = 6. 84.714
Ans.97.(b) Let x gm of water be taken Ans.106.(d) Last three digits must be
Then, Gold = 19x gm & Copper = 9x gm. divided by 8.
Let 1 gm of gold be mixed with y gm of Ans.107.(d) Let x be the number
Copper. 14% of x = 105 ⇒ x = 750.
Then, 19x + 9xy = 15x (1 + y) Ans.108.(b) In one minute,
FG 2IJ 1 1 1 1 11 1 7
⇒y =
H 3K + + − = −
10 20 30 15 60 15 60
=
Ans.98.(a) (1502)2 − (1498)2 of the tank can be filled.
= (1502 − 1498) (1502 + 1498) ∴Whole tank will be filled in
= 4 × 3000 = 12000.
60 4
3 = 8 minutes.
Ans.99.(b) of 480 ÷ 8 + 82 = ? 7 7
5 1
x x
3 1 Ans.109.(c) × 3 = 192
∴? =
5 × 480 × 8 + 64
⇒ x = 24
= 36 + 64 = 100
Ans.110.(d) Given expression
Ans.100.(a) 64 ÷ 8 ÷ 4 ÷ 2
0.152
= 8 ÷4 ÷2 = 2 ÷2 = 1 =
0.25 + 0.09 − 0.15
a 2 b 5
Ans.101.(c) = , = 0.152 152 8
b 3 c 7 = = = = 0.8
a b c 0.19 190 10
⇒ = =
10 15 21 Ans.111.(c) Given expression
Ans.102.(d) Let the two numbers be 5K
and 7K. 0.01 + 0.08 0.09 0.3
= = = = 100
∴L C M of 5 K and 7 K = 35 K 0.003 0.003 0.003

24. Practice Paper (Solved) ] [ QA – 24
Ans.112.(a) 11
∴Remaining of the bucket is filled
20
2 1 3
of of 25.20 = K × of 36 11
3 4 2 by tap B in 15 × = 8 minutes 15
20
⇒ 4.2 = 54 K seconds.
42 7 Ans.119.(a) A, B and C's shares in the
⇒ K= =
540 90 capital are in the ratio of 12000 × 24 :
LM R FG IJ UOP
16000 × 24 : 15000 × 16 ,
NM S H K VQP
1 5
Ans.113.(c) 1 + 2 3 − 1 + 2 − − i.e. 288 : 384 : 240,
T 2 2 W i.e. 18 : 24 : 15,
= 1 + 2 [3 − {1 + (2 + 2)}]
i.e. 6 : 8 : 5
= 1 + 2 [3 − 5] = 1 + 2 (−2)
∴ Share of C in the profit
= 1 − 4 = −3
5
Ans.114.(a) 0.2, (.2)2 = 0.04, = × 45600 = Rs. 12000
19
1
0.2 = 0.222 , 1 ÷ 0.2 = 0.2 = 5 Ans.120.(a) Given expression
Ans.115.(a) 5% of (5% of 100)
b12.12 + 8.12gb12.12 − 8.12g
= 5% of 5 =
1
= 0.25
=
b0.25gb0.25 + 19.99g
4
LM8 OP × FH16 IK
−15 / 8
8 / 15 1/ 4
+N Q
3
Ans.116.(d) Let x = 6 + 6 + 6+.....
LMb128g OP −15/7
−1/5
⇒x = 2
6+x ⇒x = 6 + x N
3
Q
⇒ x2 − x − 6 = 0
4 8 −1 × 8 = 4 + 1 =4
1
⇒ (x − 3)(x + 2) = 0 = + 1 2
b g e j
0.25 3 3
128 7 27 7
⇒x = 3
1 1 1 1 1
− =
Ans.117.(d) In one hour,
e j e j
−
10 15 30 Ans.121.(b) 28 + 10 3 2 − 7−4 3 2
of the cistern will be empty.
Re5 + 3 j U − Re2 − U
1 -1
Ans.118.(b) Tap A and Tap B can fill = S
T V S
W T
2 2
3j V
2 2
W
1 1 2
= e5 + 3 j − e2 − 3 j
+ = −1
together of the bucket in
12 15 30
one minute.
= e5 + 3 j −
1 2+ 3
×
9 2− 3 2+ 3
In three minutes, of the bucket is
20
filled by taps A and B.
e j e
= 5+ 3 − 2+ 3 = 3 j