PERCENTAGE

1 If Sukhbeer sold 12 pen for a rupee and he had a loss of 11. The length breadth and height of the room is in 4 : 2 : 1.
20%. How many pens he sold for a rupee if he wants to If the breadth and height are one fourth of the original
make a profit of 20%. while the length is doubled, then, the total area of the
(a) 8 (b) 9 four wall of the room will …….
(c) Can’t be determined (d) 10 (a) remain the same (b) decrease by 60%
2
3
Sahnaaz spends of his salary. Now his salary increased (c) decrease by 64.5% (d) decrease by 66.2%
4
12. A student took five papers in an examination, where the
by 20% and his expenditure is increased by 10%. Find
full marks of first two paper is 100 and for last three is
out the percentage increment in his savings?
150. His marks in these were in the proportion of 5 : 7 : 8
(a) 75% (b) 25%
: 9 : 10. In all paper together candidate got 60% of total
(c) 50% (d) Can’t be determined
marks. Then number of papers in which he got more
3 X’s salary is 20% less of y’s. Now find out how much
than 50% marks is.
percent y’s salary is more than that of x’s salary. (a) 4 (b) 3
(a) 20% (b) 40% (c) 5 (d) 6
1
(c) 16 % (d) 25% 3
13. A college has raised th of the amount it need for a new
6
4
4 How much percent the markup price of a product is charity fund by receiving an average donation of 600
greater than that of its cost price when a shopkeeper from 60% of the people. If the college is to raise exactly
gives a discount of 10% and had a profit of 17% the amount needed for the new charity fund. What
(a) 10% (b) 20% should be average remaining donation from the
(c) 30% (d) Can’t be determined remaining people which is not given?
5 Price of a commodity is increased by 20%. By what (a) 300 (b) 250
percentage the consumption of the commodity is (c) 400 (d) 500
decreased by the consumer, if the expenditure on this 14. Forty percent of the employees of a certain company are
commodity remain constant. men and 75% of the men earn more than Rs 25,000 per
2
(a) 16 % (b) 25% year. If 45% of the company’s employees earn more than
3
(c) 15% (d) 8% Rs. 25,000 per year, what fraction of the women
6 The tank-full of petrol in Anil’s car lasts for 10 days. If he employed by the company earn maximum of Rs 25,000
starts using 25% more everyday. How many days will per year?
the tank full of petrol last? (a) 2/11 (b) 1/4
(a) 5 (b) 6 (c) 1/3 (d) 3/4
(c) 7 (d) 8 15. One amoeba splits into 16 amoeba of the next
7 In an XII class examination out of 480 students, 85% of generation, but due to environment only 25% of one
the girls and 70% of the boys passed. How many girls generation can produce the next generation. If the
appeared in the examination. If total pass percentage seventh generation number is 4096 million, what is the
was 75%. number in first generation.
(a) 320 (b) 160 (a) 0.25 million (b) 1 million
(c) 4 million (d) 16 million
(c) 370 (d) 120
8 An Alloy of Zinc and Iron weighs 50gm. It contains 80%
zinc. How much zinc should be added to the alloy, so that
percentage of zinc is increased to 90%?
(a) 50 gm (b) 60 gm
(c) 30 gm (d) 45 gm
9 The profit percentage of a product when it is sold for Rs.
1128 is equal to the loss percentage when the product is
sold for Rs. 872. Find the cost price of the product.
(a) 1000 (b) 928
(c) 1100 (d) Can’t be determined
10 If the price of a commodity is decreased by 10%, then it
is increased by 10%. Find out the final percentage
change in the price of a commodity.
(a) No change (b) 1% decreased
(c) 1% increased (d) Can’t be determined.

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16. A man earn 𝑥% on the first Rs. 2000 and 𝑦% on the rest 24. Using only 2, 5, 10, 25 and 50 paise coins, what will be
of his income. If he earns Rs. 700 from Rs. 4000 and 900 the minimum number of coins required to pay exactly 78
from Rs. 5000 of income. How much he earn in the paise, 69 paise and Rs. 1.01 to three different persons?
income of Rs. 11000. (a) 19 (b) 20
(a) 2400 Rs. (b) 2300 Rs. (c) 17 (d) 18
(c) 2200 Rs. (d) 2100 Rs. 25. From each of two given numbers, half of the smaller
17. The rate of increase of the price of petrol per year number is subtracted so the larger one is three times the
observed to be two percent more than inflation rate smaller. By what percent larger number is greater than
expressed in percentage. The price of petrol on January the smaller number.
1, 1994 is 40 Rs. per litre. The inflation rate of the year (a) 50% (b) 100%
from 1994 to 1996 expected to be 8% each year. The (c) 150% (d) 200%
expected price of petrol per litre on January 1, 1997
would be SOLUTIONS
(a) 52 Rs. (b) 52.5 Rs.
(c) 53.24 Rs. (d) 54 Rs. 1. (a) In starting he has a loss of 20%
80
18. A report consists of 20 sheets each of 55 lines and each ∴ CP × = SP1 …(1)
100
such line consists of 65 characters. This report is 1
and S.P1. of a pen =
reduced onto sheets each of 65 lines such that each line 12
consists of 70 characters. The percentage reduction in put this value in equation(1)
80 1
number of sheets is closest to CP × =
100 12
(a) 20% (b) 5% CP = ×
1 100
12 80
(c) 30% (d) 35%
Now he wants a profit of 20%
19. A milkman mixes 20L of water with 80L of milk. After 120
selling one fourth of this mixture he add water to ∴ CP × = SP2
100
1 100 120
replenish quantity that he has sold. What is the current × × = SP2
12 80 100
proportion of water to milk? 1
SP2 =
(a) 2 : 3 (b) 1 : 2 8

(c) 1 : 3 (d) 3 : 4 Now he will sell 8 pen for a rupee.

20. A piece of string is 40 cm long. It is cut into three pieces. 2. (c) Let his salary is 100
3
The longest piece is 3 time as long as the middle-sized He spends × 100 = 75
4
and the shortest piece is 23 cm shorter than the longest His savings is 25
piece. By how much percentage longest piece is greater Now increased salary = 120
10
than the shortest piece. New expenditure = 75 + 75 × = 82.5
100
(a) 125% (b) 300% Now savings = 120 – 82.5 = 37.5
(c) 600% (d) 575% 37.5 − 25
Percentage increment in saving = × 100
21. Instead of walking along two adjacent sides of a 12.5
25

rectangular field, a boy took a short cut along the = × 100 = 50% .
25
diagonal and saved a distance equal to half the longer 3. (d) Let y’s salary = 100
side. Then, the ratio of the shorter side to the longer side 80
So x’s salary = 100 × = 80
100
is
1 2 y’s salary is greater than x by 20
(a) (b) difference in salary
2 3 In percentage = ′ × 100
1 3 X salary
(c) (d) 20
4 4 = × 100 = 25%
22. Fresh grapes contain 90% water by weight while dried 80

grape contain 20% water by weight. What is percentage

of reduction in weight of dried grapes from the fresh
grape.
(a) 33.3% (b) 66.6%
(c) 25% (d) 87.5%
23. You can collect rubies and emeralds as many as you can.
Each ruby is of Rs 4 crore and each emerald is of Rs 5
crore. Each ruby weighs 0.3 kg. And each emerald
weighs 0.4 kg. Your bag can carry at the most 12 kg.
What you should collect to get the maximum wealth?
(a) 20 rubies and 15 emeralds
(b) 40 rubies
(c) 28 rubies and 9 emeralds/
(d) None of these

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4. (c) Let the C.P = 100 11. (c); Let the original length, breadth and height of the
117 room are 4𝑥, 2𝑥 and 𝑥 respectively.
SP = CP ×
100
Area of four wall = height× (perimeter of base)
S.P = 117
90 = 𝑥 × 12𝑥 = 12𝑥 2
Markup price × = 117 1 1
100 New length, breadth and height are 8𝑥, 𝑥, 𝑥
117 × 100 2 4
= respectively (according to question given)
90
1 1
Markup price = 130. So, new area of the four wall = 𝑥 (8𝑥 + 𝑥)
2 2
So it is 30% greater than C.P. 17
= 𝑥2
5. (a) Formula of successively percentage change 4
ab 17𝑥2
12𝑥 2 −
=a+b+ % decrease in area = 4
× 100
100
12𝑥 2
Here the final change is zero. =64.5%
ab
So a + b + =0 12. (a); Maximum marks in total subject
100
Here a = 20% and b = x% = 100 × 2 + 150 × 3
20 × 𝑥 = 650
20 + x + =0 650 × 60
1
100 Student got =
100
𝑥 [1 + ] = −20 = 390
5
6
𝑥 [ ] = −20 39x = 390
5
−100 X = 10
= Student marks in five subject is 50, 70, 80, 90 and 100
6
2
= −16 % So, except first subject (50 mark), student got more than
3
2 50% mark in each subject.
= 16 % decreased. 13. (a); Let total number of people = 𝑥
3
6. (d) Let in starting he uses 10 lit. a day. 3 60𝑥
𝑡ℎ of raised fund = 600 ×
4 100
So total fuel capacity of tank = 10 × 10 = 100 lit
= 360𝑥
Now use is increased by 25% 1 360𝑥 4
125 So, 𝑡ℎ of the raised fund = × = 120𝑥
Now he uses petrol = 10 × = 12.5 lit a day 4 3 4
100 According to question given,
Total fuel
Number of days = 120𝑥 = (average fund) × Number of people which is not
use in a day
100 given
= = 8 days. 40
12.5 120𝑥 = average fund × 𝑥
7. (b) 85% of the girls passed and 70% of the boys passed 100

marks 75% of students passed. Average fund = 300 Rs.

14. (d); Let number of man and women be 40 and 60
respectively.
∴ Number of men earning more than Rs 25,000 = 30
Total number of employees earning more than Rs 25,000
= 45
∴ Number of women earning more than Rs 25,000
= (45 – 30) = 15
Now, fraction of the women earning Rs. 25,000 or less
60−15 45 3
= = =
60 60 4
x + 2x = 420 15. (b); Let the first generation number = 𝑥
3x = 480 According to question given,
x = 160
∴ Number of girls = 160.
80
8. (a) Zinc present in Alloy = × 50 = 40 gm.
100
Now we need to make it 90% It mean after one generation number become 4 time of
40 + 𝑥 90
= first generation
50 + 𝑥 100
400 + 10x = 450 + 9x So 𝑥(4)6 = 4096
x = 50 𝑥 = 1 million
So we needed 50 gm of zinc. 16. (d); According to question given,
𝑥 𝑦
9. (a) C.P =
1128 + 872 × 2000 + × 2000 = 700 …(1)
100 100
2 𝑥 𝑦
2000 × 2000 + × 3000 = 900 …(2)
= = Rs. 1000 100 100
2
ab From (1) and (2)
10. (b) Final percentage change = a + b + 𝑥 = 15%
100
10 × 10 𝑦 = 20%
= 10 – 10 – = −1
100 15 20
= 1% decreased. ⇒ × 2000 + × 9000 = 2100 Rs.
100 100

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17. (c); Price increase per year = 2% + 8% = 10% 22. (d); Let the weight of fresh grape = 100 kg
So price of petrol per litre on 1 January 1997 Water content in fresh grape = 90 kg
= 40 × 1.1 × 1.1 × 1.1 = 53.24 Rs. In dried grapes 80% is the dry part which is = 10kg
18. (a); Total number of characters = 20 × 55 × 65 = 71500 So weight of dried grapes = 10*100/80
Number of pages required, if the report is retyped = 100/8 kg
100
71500 100 −
8
= = 15.70 % reduction = ∗ 100 = 87.5%
65×70 100
4
Hence, 16 pages are required. Hence, % reduction 23. (b); Price of each kg ruby = crore
3
20−16
= × 100 = 20%. = 13.33 crore
20 5
19. (a); Initially milkman has 100 litre at mixture Price of each kg emerald = = 12.5 crore
4
After selling one fourth and adding water to replenish Price of ruby > price of emerald.
Quantity For maximizing wealth you can only purchase ruby.
milk : water = 60 : 15 + 25 Hence, option (b) would be correct.
= 60 : 40 ⇒ 6 : 4 24. (a); Minimum number of coin required to pay exactly 78
paise
Hence, current proportion of water and milk = 4 : 6
= 1 × 50 + 10 × 2 + 2 × 4
=2:3
= 7 coin
20. (d); Let middle-sized piece in long = 𝑥 cm. To pay exactly 69 paise
Longest length of piece = 3𝑥 cm. = 1 × 50 + 1 × 10 + 1 × 5 + 2 × 2
And shortest piece = 3𝑥 − 23 cm. = 5 coin
According to question given, To pay exactly 1.01 = 50 × 1 + 25 × 1 + 10 × 2 + 2 × 3
𝑥 + 3𝑥 + 3𝑥 − 23 = 40 = 7 coin
7𝑥 = 63 Total coin = 19 coin.
𝑥 = 9 cm. 25. (b); Let the larger number = 𝑦
So, longest piece = 27 cm. Smaller number = 𝑥
According to question given,
Shortest piece = 4 cm. 𝑥 𝑥
required % =
23
× 100 = 575% (𝑦 − ) = 3 (𝑥 − )
4 2 2
4𝑥
21. (d); Let longer side be-a 𝑦=
And smaller side be-b 2
𝑦 = 2𝑥
𝑦−𝑥 2𝑥 − 𝑥
Required % = = = 100%
𝑥 𝑥

According to question given,

𝑎
𝑎 + 𝑏 − √𝑎2 + 𝑏 2 = (Suppose a in the length of the
2
longer side)
𝑎
+ 𝑏 = √𝑎 2 + 𝑏 2
2
𝑎2
= + 𝑏 2 + 𝑎𝑏 = 𝑎2 + 𝑏 2
4
3𝑎2 𝑎 4
𝑎𝑏 = ⇒ =
4 𝑏 3
𝑏 3
Required ratio =
𝑎 4

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