The document contains solutions to math problems involving percentages. It provides the answers and step-by-step workings for each problem. The problems cover a range of concepts including ratios, proportions, percentage increase/decrease, and calculating original values from final amounts.

1. 1 Ans: c
Solution: The weight of non-water in 20 kg of fresh grapes (which is 100-90=10% of whole
weight) will be the same as the weight of non-water in x kg of dried grapes (which is 100-
20=80% of whole weight), so 20∗0.1=x∗0.820∗0.1=x∗0.8 --> x=2.5x=2.5
2 Ans:a
Solution: Let the number be x
So x - 0 .7 x = 81
 X = 270 , so 2/5th of this number will be 108
3 Ans: d
Solution: time spent on flow chart = 48 x ¼ = 12 hrs.
Time spent on coding = 48 x 3/8 = 18 hrs
So time left for debugging = 48 – 12- 18 = 18 hrs
4. Ans: d
Solution: total business = 75000 x 3/2 x 4/3 =150,000
5. Ans:d
Solution: Let total income be X,
So X – 20000 –( X – 20000)/2 = 6000
 X = 32000
6. Ans:c
Solution: Let the cheques on Monday be x, so on Tuesday they will be 3x.
So x + 3x + 4000 = 16000 => x = 3000
So on Tuesday = 3 x 3000 = 9000
10 Ans: [d]
Solution: If Weightof Rani=R,Meena=M, Tara=T
Given,R=(25M/100)=(40T/100) or R=(M/4)=(2T/5), M=8T/5
% of Tara's weighttoMeena'sweight=100*8T/5=160
11 Ans: [b]
Solution: PresentWorth= x/(1+R/100)^n
640=1024/(1+R/100)
R=60%
after1 yearvalue=250/(1+60/100)=156.25
12 Ans: [a]
Solution: net percentage change = 15 +(– 25)+ [{(15*(-25)}/100]
= -10-3.73 = -13.75. –ve sign decrease in the price.
13 Ans: [d]
Solution: Lets assume cost price of T.V = Rs. 100
so,marked price of T.V = Rs. 75
=> Final price = 120% of 75 = Rs. 90
Hence, Decrease in price = (100-90) = 10
Decrease by 10%.
14 Ans: [b]
Solution: Difference
(65% - 35%)v = 15000
v = 15000/.3
v = 50000

2. Total votes cast = 50000
Winner
65% * 50000 = 32500 votes
15 Ans: [C]
Solution: 70% passed in english so fail in english 30%
75% passed in hindi so fail in hindi 25%
so total fail %= 55%
but 20 % fail in both that means 20 % included in both 30% fail in english and 25
% fail in hindi
but we have to count students only once so we have to subtract 20% from 55%
55%-20%=35%
so total failure %=35%
so total pass %=65%
Given that students pass in both subj are 260 i.e total pass studenys are 260
let total students be x
so 65% of x=260
x=400
16 Ans: [C]
Solution: Area= radius *radius*pi
Let the radius= 10
Area= 100pi
Reduced radious= 9
Area= 81pi
Change in radius =(100-81)pi=19pi
% change in radius =(19pi/100pi)*100=19
17. Ans: [B]
Solution: Ans: 11 1/9 %= 11 1/9%
Let the price of the article = Rs.100
New price = 100 - 10 = 90
Therefore the new price must be increased by
(100−90)×100/90=100/9%=11 1/9%
18. Ans: []
Solution:
19. Ans: [B]
Solution: Let the two numbers be x and y.
3x = 1.2( 2y +105)
3x = 2.4y +126 ………………..(1)
2x +36 = 0.8(3y)
2x +36 =2.4y ………………..(2)
x = 162
20. Ans: []
Solution:

3. 21. Ans: [C]
Solution: 2/3 of 1/3 of X = 3/5 of 5/9 of Y
X/Y =3/2
22. Ans: [C]
Solution: Let total = X
Pass Marks = 40% of X – 14..........1
Pass Marks = 30% of X + 16 ..........2
Equate 1 and 2
X = 300
23. Ans: [C]
Solution: Total = 1600
Girls = ¼ of 1600 = 400 therefore Boys = 1200
50% girls failed = 200
75% boys passed i.e. 25% is failure
Failed Boys = 25% of 1200 = 300
Failure % =( 200+300)*100/1600 = 31 ¼
24. Ans: [C]
Solution: increased by 25% i.e. ¼, so it will decrease by 1/5= 20%
Increase by 20% i.e. 1/5, so it will decrease by 1/ 6= 16 2/3
25. Ans: [C]
Solution: 20% of 2/5 th of X = 60 ml
X= (60*5*100)/(2*20) = 750ml
26. Ans: []
Solution:
27. Ans: [A]
Solution: Total no of legal connection = 80% of 90% of x
i.e. 72% of X
therefore illegal connection is 28% of x
28. Ans: [A]
Solution: Remaining % = 100-(20+10+9+7)
= 100-46 = 54%
LET total = x
i.e 54% of x = 2700
x = 5000Rs
29. Ans: []
Solution:
30. Ans: [C]
Solution: Let quantity be X
Price = 200Rs Increase in Price = 10%
New Price = 110% of 200 = 220Rs
ATQ 200x = 220(x-2)
200x = 220x – 440
X = 22 ANS 100/11, 10
31. Ans: []
Solution:

4. 32. Ans: [D]
Solution: let x and y be the sides of the rectangle then
correct area = (110/100)x * (95/100)y
=1.045xy – xy = .045xy
Error% = .045xy * (1/xy) * 100%
= 4.5%
33. Ans: [B]
Solution: Decreased by 25% = ¼ = 1/n
Increased in working time by 1/n-1 = 1/3
1/3 = 33 1/3
34. Ans: [D]
Solution: let x/y be the original value
then A.T.Q : (x+.25x)/(y-.2y) = 5/4
==>(1.25x/0.8y)=5/4
==>x/y= 4/5
35. Ans: []
Solution:
36. Ans: [A]
Solution: Let the area of original square = 100
Then, side = 10
New length = 150% of 10 = 15, New breadth = 120% of 10 = 12
New area = 15*12 = 156
Therefore
Increase is area = 80%