Quantitative apptitude question

1. Page 1LPU Set - 1
LPU Set - 1
Quantitative Aptitude
1. A bottle of whisky contains
3
4
of whisky and
the rest is water. How much of the mixture
must be taken away and substituted by equal
quantity of water so as to have half whisky
and half water?
(a) 25% (b) 45%
(c)
1
33 %
3
(d) 50%
2. A man covered a total distance of 1,000 km
in 16 hr, partly in a taxi at 36 km/hr and partly
in a bus at 80 km/hr. The distance covered
by the bus is (approx.)
(a) 770 km (b) 640 km
(c) 720 km (d) 680 km
3. In what ratio must the 1 : 4 mixture of whisky
and water be mixed with a 1 : 1 mixture to
obtain a 2 : 3 mixture?
(a) 2 : 3 (b) 3 : 2
(c) 2 : 1 (d) 1 : 2
4. An alloy of copper and tin contains 77.78%
of copper. After 18 kg of tin is added, the
copper content gets reduced to 50%. How
much copper and tin respectively does the
new alloy have?
(a) 40 kg and 15 kg (b) 25.2 kg and 20 kg
(c) 20 kg and 23 kg (d) None of these
5. A container contains 80 kg milk. From this,
8 kg milk was taken out and replaced by
water. This process is repeated thrice. What
is the ratio of the quantity of milk after the
first draw to quantity of milk left after the third
draw?
(a) 10 : 9 (b) 100 : 81
(c) 100 : 64 (d) 81 : 64
6. In a mixture of 35 L, the ratio of milk to water
is 4 : 1. If 7 L water is added to the mixture,
the ratio of milk to water changes to a new
ratio. If we want the ratio of milk to water to
change back to the original value, how much
milk is to be added now?
(a) 35 L (b) 28 L
(c) 21 L (d) 32 L
7. A milk vendor sells 33 L milk containing milk
and water in the ratio 12 : 1. He wants to
make this a 11 : 2 solution of milk and water
and to sell the entire quantity at the cost
price. How much of water needs to be added?
(a) 3 L (b)
9
2 L
11
 
 
 
(c) 2.5 L (d) 4 L
8. Nupur has 73 L wine in a drum. She replaces
3.65 L of it with water and keeps doing so till
the time the concentration of wine is less
than 85%. The minimum number of operations
that Nupur has to perform is
(a) 3 (b) 4
(c) 2 (d) once
9. The ratio of incomes of Rashmi and Divya is
3 : 5 and the ratio of their expenditures is 2 :
3. Who does save more? (You have to
assume that no one takes any loan from
anywhere.)
(a) Rashmi
(b) Divya
(c) Both save equally
(d) Depends upon the incomes of Rashmi
and Divya.
No of questions: 60 Marks for correct answer: 3
Time: 90 minutes Negative mark: 1

2. Page 2 LPU Set - 1
10. Ratio of incomes of Rohit and Sunil is 5 : 7
and the ratio of their expenditures is also
5 : 7. What is the ratio of their savings?
(a) 2 : 3
(b) 7 : 5
(c) 5 : 7
(d) Cannot be determined
11. The ratio of sum of squares of first n natural
numbers to square of sum of first n natural
numbers is 17 : 325. The value of n is
(a) 15 (b) 25
(c) 35 (d) 30
12. IBM and SGI quote for a tender. On the tender
opening day, IBM realizes that their
quotations are in the ratio 7 : 4 and hence
decreases its price during negotiations to
make it Rs.1 lakh lower than SGI’s quoted
price. SGI then realizes that the final quotes
of the two were in the ratio 3 : 4. What was
the price at which IBM won the bid?
(a) Rs. 7 lakh (b) Rs. 4 lakh
(c) Rs. 3 lakh (d) Rs. 1 lakh
13. A tea trader mixed two varieties of tea, one
costing Rs. 3.50 per kilogram, and the other
costing Rs. 4 per kilogram, and sells 40 kg of
the mixture to a vendor at Rs. 4.50 per
kilogram, and makes a profit of 20%. How
much of each variety did the vendor mix?
(a) 30 kg, 10 kg (b) 20 kg, 20 kg
(c) 10 kg, 30 kg (d) 15 kg, 25 kg
14. Each tree in a forest houses at least one bird.
On half the number of trees, there are 2
sparrows each, on
1
4
of the remaining there
is one pigeon each, and the rest, that housed
4 birds each, are cut off for factory use. If
there were in all 630 birds in the forest, how
many trees were cut off?
(a) 90 (b) 80
(c) 110 (d) 180
15. The total surface area of a solid copper cube
and a solid zinc cuboid are the same. The
length, breadth and height of the cuboid are
in the ratio 1 : 2 : 4. Both are melted together
in a vessel. What is the ratio of copper and
zinc in the resultant mixture?
(a)
3
214
: 8
3
 
 
 
(b)
3
214
8 :
3
 
 
 
(c)
3
23
: 8
14
 
 
 
(d)
3
23
8 :
14
 
 
 
16. In a cage, there are sparrows, parrots and
doves in the ratio 3 : 7 : 5. If the number of
parrots was more than the number of
sparrows by a multiple of both 9 and 7, what
is the minimum number of birds in the cage?
(a) 945 (b) 630
(c) 252 (d) 238
17. The price of a precious stone is proportional
to its weight. What will be the loss incurred,
if a stone weighing 28 g and costing Rs.
28,000 breaks into two pieces whose weights
are in the ratio 15 : 13?
(a) Rs. 12,000 (b) Rs. 7,000
(c) Rs. 21,000 (d) None of these
18. A housewife has 1 L of solution that contains
milk and water in the ratio 3 : 1. She adds
250 ml of 3 : 2 solution of milk and water to it
and then uses 250 ml of the combined mixture
to make curd. How much of pure milk is she
left with?
(a) 1,000 ml (b) 912.5 ml
(c) 750 ml (d) 720 ml
19. Monthly incomes of two persons are in the
ratio 5 : 4 and their monthly expenditure are
in the ratio 9 : 7. If each person saves
Rs. 500 per month, then what are their monthly
incomes?
(a) Rs. 8,000 and Rs. 10,000
(b) Rs. 3,750 and Rs. 3,000
(c) Rs. 4,500 and Rs. 3,500
(d) Rs. 5,000 and Rs. 4,000

3. Page 3LPU Set - 1
20. A, B and C started a business in which B
and C were sleeping partners. They invested
Rs. 4,000, Rs. 3,000 and Rs. 7,000
respectively for a period of one year. A is paid
10% of the profit as compensation for his
work, and then the rest is shared in the ratio
of their investments among all the three. If A
gets Rs. 6,000, as his share of profit, find out
the amount that B and C together receive.
(a) Rs. 9,000 (b) Rs. 7,500
(c) Rs. 9,600 (d) Rs. 10,800
21. What strength of 20 ml alcohol should be
added to 10 ml of 50% alcohol to get an
average strength of 20% alcohol?
(a) 0.5% (b) 5%
(c) 50% (d) 5.5%
22. A 20% hike in bus fare resulted in a 10% fall
in the passenger traffic. Still the daily
collection at the bus depot increased by
Rs. 150. The daily collection at the depot after
the fare hike is
(a) Rs. 1,600 (b) Rs. 1,750
(c) Rs. 2,025 (d) Rs. 1,875
23. 30% of the students in a class wear
spectacles. 10% of the students who wear
spectacles, wear gold-rimmed spectacles. If
the class has 200 students, how many wear
gold rimmed spectacles?
(a) 6 (b) 7
(c) 8 (d) 3 e. None of these
24. In a village, 18% of the population are children
and 10% of children are female. If the number
of female children is 90, what is the
population?
(a) 500 (b) 5,000
(c) 600 (d) 6,000
25. A market leader wants to make profit by selling
rice. He tried different methods to get higher
profit. Find out which among the following
methods should he use to maximise his profit.
I : Increase the price by 5% and reduce
the weight by 5%
II : Mix impurities to the extent of 10%
of the weight of rice
III : Use a weight of 900 g in stead of 1 kg
IV : Sell rice at 10% profit
(a) I or III (b) II or III
(c) II or IV (d) None of these
26. A dishonest seller uses a weight of 800 g in
place of 1 kg and adds 20% impurities in
sugar. What would be his profit percentage if
he claims to be selling at cost price?
(a) 50% (b) 40%
(c) 45.5% (d) 36%
27. A sum of money amounts to Rs. 1,180 and
Rs. 1,300 in 3 years and 5 years respectively
at a simple interest per annum. The money
invested is
(a) Rs. 90 (b) Rs. 950
(c) Rs. 1,000 (d) Rs. 1,050
28. If the cost price of 6 articles is the same as
the selling price of 5 articles, the profit
will be
(a) 25% (b)
1
22 %
2
(c) 20% (d)
3
18 %
4
29. One kilogram tea and 1 kg sugar together
cost Rs. 95. If the price of tea falls by 10%
and that of sugar rises by 20%, the price of
1 kg each combined comes to Rs. 90. The
original price of tea per kilogram is
(a) Rs. 72 (b) Rs. 55
(c) Rs. 60 (d) Rs. 80
30. A showroom owner sells a leather jacket for
Rs. x and claims to make a 10% profit. He
plans to have a stall in the trade fair and mark
the same jacket at Rs. 2x. At the stall, he
allows a 20% discount. What will be the
percentage profit he makes at the trade fair?
(a) 80% (b) 60%
(c) 76% (d) 70%

4. Page 4 LPU Set - 1
31. Madhu got married 6 years ago. Today her
age is 125% times her age at the time of
marriage. Her son’s age is one-tenth of her
age. Her son’s age is
(a) 3 years (b) 2.5 years
(c) 2 years (d) 4 years
32. A building worth Rs. 13,31,000 is constructed
on land worth Rs. 7,29,000. After how many
years will the value of both be same if land
appreciates at 10% and building depreciates
at 10% per annum?
(a) 1.5 years (b) 3 years
(c) 2 years (d) 2.5 years
33. In a village the current birth rate per thousand
is 55 whereas corresponding death rate is
34 per thousand. The net growth rate in terms
of population increase will be
(a) 0.021% (b) 0.0021%
(c) 21% (d) 2.1%
34. The population of a town was 8,000. In one
year, the female population increased by 8%
and the male population increased by 10%,
but the total increased by only 9%. What is
the number of males in the town now?
(a) 4,400 (b) 4,000
(c) 5,000 (d) 6,000
35. A sum of money doubles itself at compound
interest in 15 years. In how many years will it
become eight times?
(a) 30 years (b) 45 years
(c) 50 years (d) 60 years
36. CI on a sum for 2 years at 4% per annum is
Rs. 102. The SI on the same sum for the
same period at the same rate will be
(a) Rs. 99 (b) Rs. 101
(c) Rs. 100 (d) Rs. 93
37. If CP of 36 books is equal to SP of 30 books,
then the gain percentage is
(You have to assume that all the books cost
same.)
(a) 20% (b)
4
16 %
6
(c) 16% (d)
2
8 %
6
38. A trader bought 10 kg oranges for Rs. 405, of
which 1 kg was found rotten. If he wishes to
make a profit of 10%, at what rate per kilogram
should he sell the remaining oranges?
(a) Rs. 44.55 (b) Rs. 48.66
(c) Rs. 51.25 (d) None of these
39. A man buys 6 dozen eggs for Rs. 10.80, and
12 eggs are found rotten and the rest are sold
at 5 eggs per rupee. Find his percentage gain
or loss.
(a)
1
11 %
9
gain (b)
1
11 %
9
loss
(c)
1
9 %
11
gain (d)
1
9 %
11
loss
40. A bank lent Rs. 4,000 to a person A at a certain
rate of simple interest and Rs. 5,000 to B at
1
%
2
more than that of A. After 2 years the
bank received Rs. 860 as interest from A and
B. Find the rate of interest per annum at which
the amount was lent to B.
(a) 5% (b) 4.5%
(c) 5.5% (d) 4%
41. If a snail creeps 2 ft 3 inches up a pole in first
12 hr and slips down 1 ft 4 inches in
subsequent 12 hr, how many hours will it take
to get to the top of the pole, if the height of
the pole is 25 ft?
(a) 500 hr (b) 523.93 hr
(c) 595.2 hr (d) 611.11 hr
42. A train travelling at the rate of 18.5 mph started
at 7 a.m. on a journey of 148 miles. Another
train started from the same station and arrived
15 min after the first one. If the ratio of the
speeds of the second train to that of the first
is 8 : 5, when did the second train start?

5. Page 5LPU Set - 1
(a) 10 a.m. (b) 10.15 a.m.
(c) 11 a.m. (d) 9.30 a.m.
43. Two places A and B are separated by a
distance of 200 m. Ajay and Mallu have to
start simultaneously from A, go to B and
return to A. In 10 s they meet at a place 10
m from B. If Ajay is faster than Mallu, in how
much time, after they start, will Ajay return
to A?
(a) 19 s (b)
200
s
21
(c)
400
21
s (d) 18 s
44. An athlete runs from A to B and returns at 10
km/hr, while another athlete simultaneously
runs from B to A and goes back at 15 km/hr.
If they cross each other for the first time 12
min after they start, they will next cross each
other after
(a) 18 min (b) 30 min
(c) 24 min (d) 36 min
45. At 3 p.m. every day, a man leaves New York
for Delhi and at the same time, a man leaves
Delhi for New York. Both take the same route.
The travel time for each person being 384 hr,
how many persons from New York will each
man from Delhi meet?
(a) 16 (b) 17
(c) 34 (d) 33
46. The diameter of a roadroller is 42 cm and its
length is 100 cm. It takes 400 complete
revolutions, moving only once over any
stretch, to level the certain stretch of a road.
If the cost of levelling is Rs. 10 per square
metre, then the total cost of levelling works
out to
(a) Rs. 52,80,000 (b) Rs. 6,970
(c) Rs. 5,280 (d) Rs. 4,980
47. A cycled from P to Q at the rate of 10 km/hr
and returned at the rate of 9 km/hr. B cycled
both ways at 12 km/hr. For the entire journey,
A took 10 min longer than B. Thus, the
distance PQ is
(a) 7.5 km (b) 3.5 km
(c) 2.25 km (d) 3.75 km
Directions for questions 48 and 49: Answer the
questions based on the following information.
A thief flees from Tihar Jail in a Gypsy towards Jaipur
on a stretch of straight road of 300 km long at 60
km/hr. 15 min later a police party (Sigma-Z) leaves
Tihar Jail chasing the thief at 65 km/hr.
48. How long, after the chase starts, does it take
Sigma-Z to catch the thief?
(a) 2 hr 30 min (b) 2 hr 45 min
(c) 3 hr (d) 3 hr 15 min
49. If another police party (Zigma-S) were to leave
Jaipur at 60 km/hr at the same time as Sigma-
Z leaves Tihar Jail to catch the thief, then
which of the following statement is true?
(a) Sigma-Z takes 37.5 min more than Zigma-
S in catching the thief
(b) Zigma-S reaches 37.5 min after Sigma-Z
has caught the thief
(c) Sigma-Z and Zigma-S caught the thief
together
(d) Sigma-Z was 3.375 km from the thief
when the thief was caught
50. A boat takes 2 hr to go from port A to port B
and 3 hr for the return journey. What is the
speed of the river? (Assume that speed of
the boat in still water and speed of the river
remains constant.)
(a) 2.5 km/hr
(b) 1.75 km/hr
(c) 0.5 km/hr
(d) Cannot be determined
51. P and Q are two places on the same side of
the bank of a uniformly flowing river. A person
can row from P to Q in 1 hr and from Q to P in
4 hr. Find the ratio of speeds of the boat in
still water to that of the river.
(a) 5 : 3 (b) 5 : 2
(c) 4 : 3 (d) 2 : 1

6. Page 6 LPU Set - 1
52. A man rows a boat at a speed of 5 km/hr in
still water. Find the speed of a river if it takes
him 1 hr to row a boat to a place 2.4 km away
and return back.
(a) 5 km/hr (b) 6 km/hr
(c) 3 km/hr (d) 1 km/hr
53. A motor boat sets down a river at the same
time as a country raft in the same direction
and from the same point. The motor boat
travels
40
km
3
and then without stopping it
travels
28
3
km in the reverse direction and
meets the raft. What is the ratio of speed of
the motor boat in still water to speed of river?
(a) 4 (b)
20
3
(c)
17
3
(d)
10
3
Directions for questions 54 and 55: Answer the
questions based on the following information.
Two persons, X and Y, start together from the same
point and run on a 4 km circular track in a race of 16
km. The ratio of their speeds is 3 : 7.
54. How often do they meet on the track in the
race, if they both run in the clockwise
direction?
(a) Once (b) Twice
(c) Thrice (d) Five times
55. How often do they meet in the race if X runs
in the clockwise direction and Y in the
anticlockwise direction?
a. Twice (b) Thrice
(c) Four times (d) Five times
56. At what time between 7 and 8 o’clock are the
hour and minute hands of a clock together?
(a)
1
61
11
min past 7 (b)
7
43
11
min past 7
(c)
2
31
11
min past 7 (d)
2
38
11
min past 7
57. A photocopier copies 1,500 workbooks in 8
hr, while another takes 12 hr to do the same
job. How many hours would both photocopiers
take working together to complete 1,500
workbooks?
(a) 4.8 hr (b) 4.4 hr
(c) 5 hr (d) 4.6 hr
Directions for questions 58 and 59: Answer the
questions based on the following information.
Pipe A fills a tank at the rate of 60 m3/hr. Pipe B fills
the tank in 6 hr. If both the pipes are opened
simultaneously, the tank is filled in 4 hr.
58. What is the volume of the tank?
(a) 360 m3 (b) 240 m3
(c) 720 m3 (d) 480 m3
59. A third pipe C can empty the tank in 8 hr. If
all three pipes are opened simultaneously,
how long will it take for the tank to be filled?
(a)
11
2
13
hr (b)
5
3
11
hr
(c)
5
6
13
hr (d) 8 hr
60. A and B can do a piece of work in 20 days, B
and C in 24 days, and C and A in 15 days. If
A works for 4 days, B for 8 days, and C for 8
days, then the fraction of the work completed
by them is
(a)
21
60
(b)
43
60
(c)
29
60
(d)
41
60