Questions of Percentage

Percentage:The word Percent means per hundred. Percentage is a ratio/ number which can be expressed as a part of hundred.
For the quick solving the question there are some rules of percentage given here. Read and remember it to solve the questions in a sec without pen.
1) To convert a fraction into percentage just multiply it by 100. for example \frac{1}{2} * 100 = 50%.
2) To convert a percentage into fraction just divide it by 100. for example 20% / 100 = 1/5.

3) If a number is increased by x% and y% respectively then the resultant increased percentage is

[ x + y + \frac{xy}{100} ]%.
4) If a number is first increased by x% then decreased by y% respectively then the resultant percentage is
[ x – y – \frac{xy}{100} ]%.
5) if a number is first increased by x% then decreased by x% then the resultant number is decreased by \frac{x^2}{100}
6) If A is x% more than B, then B is less than A by \frac{x * 100}{100+ x}%
7) If A is x% less than B then B is more than A by \frac{x * 100}{100 – x}%
8) If the cost of a product is increased by x% then what percent of the use of product is decreased to make the result unchanged. \frac{x}{100+x} * 100.
9) 8) If the cost of a product is decreased by x% then what percent of the use of product is increased to make the result unchanged. \frac{x}{100-x} * 100.
10) By reducing the amount of a product in x% A person purchase z kg more product in y Rupees then the reduced price is- \frac{x}{100} \frac{y}{z}.
11) If the population of city is X and there is a increment or decrement of Y% every year then after ‘t’ years the population will be x [1±\frac{R}{100}]^t
Type -1
1) Two numbers are respectively 25% and 40% less than a third number. What percentage of the first is the second? :-
a) 60, ) 70, c) 40, d) 80.

Let Third Number be 100 then First is 75 and Second is 60
So (60/75) * 100
= 80%
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2) Two numbers are respectively 20% and 50% more than a third number. These two numbers are in the ratio :-
a) 2:5, b) 4:5, c) 6:7, d) 3:5.

Let Third Number be 100 then first be 120 and second be 150
So the ratio is 120:150
i.e 4:5.
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3) 50% of (p-q) = 30% of (p+q) and q = X% of P then the value of X is:- a) 25, b) 20, c) 50, d)30.

5(p-q) = 3(p+q)
So p= 4q
i.e x= 25.
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4) If 30% of A is added to 40% of B, the answer is 80% of B. What % of A is B. a) 30%, b) 40%, c) 70%, d) 75%.

3/5 of A +2/5 of B = 4/5 of B
so A = 4/3 of B
therefor % of B in respect of A = (3/4* 100)
= 75%.
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5) If 60% of A income is equal to 75% of B’s income, then B’s income is equal to X% of A’s income. The value of X is:- a) 60, b) 70, c) 80, d) 90.

Let A’s income is 100.
So 60% of A = 60
75% of B = 60
B = 80
So B is 80% of A’s income.
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6) If a number X is 10% less than another number Y and Y is 10% more than 125, then X is equal to:- a) 150, b) 143, c) 140.55, d) 123.75.

Y = 10% more than 125
so Y = 137.5
X is 10% less then Y
X= 90% of 137.5
= 123.75.
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7) If a number is decreased by 12%, it becomes 110. What is the number:- a) 125, b) 88, c) 150, d) 220.

88% = 110
So 100 % = 110 * \frac{100}{88}
= 125.
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8) 75% of a number is added to 75 is equal to the number. The number is:- a) 150, b) 200, c) 225, d) 300.

Let no be X
75 % of X+ 75 = X
X-3x/4 = 75
X = 300

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9) If 60% of a number is subtracted from another number the second number reduces to its 52%, the ratio of the first number to the second number is:- a) 6:5, b) 5:3, c) 5:4, d) 4:5.

Let first no is X and second is Y
Y- 60% of X = 52 % of Y
Y – 52% Y = 60% of X
48% of Y = 60 % of X
so X : Y = 4 : 5.
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TYPE-2
1) Kishan spend 30% of his salary on food and donates 3% in a charitable trust. He spends Rs 2310 on these two items, then total salary for that month is:- a) 6000, b) 8000, c) 9000, d) 7000.

30% +3% = 2310
So 100 % = 2310 *\frac{100}{33}
=7000.
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2) Out of her total income, Neelam spends 20% per month on house rent and 70% of the rest on house hold expenditure. If she saves Rs 3600. What is her total income? a) Rs15000, b) Rs10500, c) Rs10000, d) Rs10050.

30% = 3600.
100% =3600 * \frac{100}{30}
Now, 80% = 3600 * \frac{100}{30}
So 100 % =3600 * \frac{100}{30} * \frac{100}{80}
Total income = 15000.
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3) Arbind spends 75% of his income and saves the rest.His income is increased by 20% and he increases his expenditure by 10%. Then the increase in savings in percentage is:- a) 48, b) 50, c) 52, d) 55.

Let Arbind income be 1000
75 % spend and 25 % save
i.e 750 spend and 250 save.
Now increased income = 120% of 1000
= 1200
increased expenditure = 110% of 750
=825
therefore new saving = 1200-825
=375
which is more than 125 of previous savings
increased saving in percentage = (125/250) * 100
= 50%

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4) A man had Rs 4800 in his locker two years ago. In the first year, he deposited 20% of the amount in his locker. In the second year, he deposited 25% of the increased amount in his locker. Find the amount at present in his locker. a) 7000, b) 7200, c) 8000, d) 8200.

In first year the total amount = (120 % of 4800)
In the second year the total amount = 125% of (120%of 4800)
= 5/4 * 6/5 * 4800
=7200
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5) If 20% of a man salary is paid as rent, 60% is living expenses and 10% is paid in L.I.C. If he spends remaining Rs 30 on the education of the children find the salary:- a) 300, b) 100/3, c) 3000, d) 900.

Remaining 10% = 30
So 100 % = 3000
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6)A person gives 10% to his wife and 10% of the remaining to hospital again 10% of the remaining to prime minister’s relief fund. Then he has only Rs 7290 With him. What was the initial sum of money with that person? a) 10000, b) 12000, c) 11000, d) 15000.

Initial Sum of money = 7290 * \frac{100*100*100}{90*90*90}
=10000
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7)After deducting 10% from a certain sum, and then 20% from the remainder, there is Rs 3600 left. Find the original sum:- a) 4000, b) 5000, c) 3000, d) 6000.

Original sum = 3600 * \frac{100*100}{80*90}
= 5000
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8)The population of a town is Rs 8000. It increases by 10% during the first year and 20% during the second year. What is the population after two years:- a) 10000, b) 12000, c) 10560, d) 15000.

The population after 2 years = 8000 * \frac{110*120}{100*100}
= 10560.
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9) The population of a village decrease at the rate of 20% per anum. If its population 2 years ago was 10,000 the present population is:- a) 4600, b) 6400, c) 7600, d) 6000.

present population = 10000 * \frac{80*80}{100*100}
6400.
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10) In a vacation course in a collage 15% seats increase annually. If there were 800 students in 2012, how many seats will be there in 2014:- a) 920, b) 1040, c) 1058, d) 1178.

In 2 years the increased seats = 800 * \frac{115*115}{100*100}
= 1058.
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Type – 3
1) In an examination, 72% of the student passed in Mathematics and 78% passed in Bengali. If none failed in both the subjects, then what % of the students passed in both the subjects? a) 45%, b) 50%, c) 5%5, d) 60%.

Failed in math = 28 %
Failed in Bengali = 22%
Now % of pass in both subject = 100-(28+22)%
50%.
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2) In an school 40% of the students play football and 50% play cricket If 18% of the students neither play football nor cricket, the % of the students playing both is:- a) 40%, b) 32%, c) 22%, d) 8%.

student not play football = 60%
student not play cricket = 50%
18 % common in both
so (60+50) – 18
92 % not playing not playing both
8 % students playing both

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3)In an examination 60% of the student pass in English, 70% pass in Hindi and 40% pass in both. What percentage of students fail in both English and Hindi:- a) 10, b)20, c) 25, d) 30.

Pass in Eng = 60%
Pass in Hindi = 70%
40 % common in both
So (70+60)% -40%=90%
(100-90)=10% fail in both.

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4) In an examination, 52% of the candidate failed in English and 42% failed in Mathematics. If 17% failed in both subjects, then % of candidates, who passed in both the subjects was:- a) 25, b) 22, c) 23, d) 21.

52% fail in Eng
42 % fail in Math
17% failed in both
So (94-17) = 77 % pass in any one
(100 – 77) = 23 % pass in both subjects.
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5)In an examination 65% of the students pass in physics, 55% pass in chemistry and 25% fail in both subjects. The percentage of students having passed in physics and Chemistry:- a) 35, b) 45, c) 55, d) 65


35 % fail in Physics
45% fail in chemistry
25 % fail in both
So (45+35)- 25 % pass in both
=55 %.
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6)In an examination, 34% of the students failed in mathematics and 42% failed in English. If 20% of the students failed in both the subjects, then the percentage of the student who passed in both the subjects was:- a) 56, b) 54, c) 50, d) 44.


34% failed in Maths
42% failed in Eng
20% failed in common
So, (34+42) – 20 =56 pass in any one
(100-56) = 44 % Pass in both.
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7)In an examination, A gets 28% of total marks and failed by 55 marks, while B gets 37% of the total marks and get 17 more than the pass marks, Find the maximum marks and those necessary for passing:- a) 700, b) 800, c) 900, d) 500.

(37-28)% = 55+17
9% = 72
100% = 72 * 100/9
=800
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8)A candidate who gets 20% marks in an examination fails by 30 marks but another candidate who gets 32% gets 42 marks more than the pass mark. Then the percentage of pass marks:- a) 33, b) 25, c) 50, d) 52.

(32-20)% = 72
100% = 600
Pass marks = 20% of 600 +30
=150
Pass % = 25

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9)For an examination it is required to get 36% of maximum marks to pass. A student got 113 marks and failed by 85 marks. The marks of the examination are:- a) 500, b) 550, c) 565, d) 620.

pass marks = 113+85
Pass % =36 %
36 % = 198
100% = 550 marks
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10)In a collage, 40% of the students were allotted Group-A, 75% of the remaining were given Group-B and the remaining 12 students were given group-C. Then the number of students who applied for the groups is:- a) 60, b) 80, c) 92, d) 100.

Number of total students = 12 * \frac{100*100}{60*25}
=80 studentts
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TYPE-4
1) The salary of a worker is first decreased by 20% and then increased by 10%. What is the percentage effect on his salary:-
a) 10%increased, b) 10%D, c) 12%Inc, d) 12%D.

-20+10-\frac{20*10}{100}
= – 8% i.e decrease.
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2) The tax of a commodity is diminished by 20% and its consumption increased by 15%. Find the effect on revenue:- a) 8%D, b) 8%Inc, c)10%D, d) 10%Inc.

Net effect = -20+15 – \frac{20*15}{100}
= -8% i.edecrease.
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3) When the price of cloth was reduced by 25%, the quantity of cloth sold increased by 20%. What was the effect on gross receipt of the shop:- a) 5%Inc, b) 5% D, c) 10%Inc, d) 10% D.

-25 + 20-\frac{25*20}{100}
= -8 % i.e decrease.
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4)The price of an item was first increased by 40% and then decreased by 20% The final price compared to the original price:- a) – 20%Less, b) 20% more, c) 12% more, d) 30% less.

40-20 –\frac{40*20}{100}
=12 % increase.
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5) If a number is increased by 25% and the resulting number is decreased by 25%, then the percentage increase finally is:- a) 25/4%Inc, b) 6% Inc, c)No change, d) 25/4% D.

25 -25 –\frac{25*25}{100}
= – 25/4 % i.e decrease.
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6) If the diameter of a circle is increased by 100%, its area is increased by :- a) 300%, b) 400%, c) 100%, d) 200%.

100+100+\frac{100*100}{100}
= 300% increase.
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7) If a container is 4/5th full and 25% of its content is lost due to evaporation, how much is the container filled now:- a) 75%, b) 60%, c) 20%, d) 50%.

Let the weight of the container is 100
4/5th is fill i.e 80 filled.
25 % of 80 is evaporate
then remaining is 60
so 60% of container is filled now.

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8) If a numerator of a number is increased by 20% and the denominator is decreased by 10% the value of the fraction is 16/21. The original fraction is:- a) 4/7, b) 5/7, c) 2/5, d) 3/5.

Let the fraction be x/y
20% increased in numerator i.e 6x/5
10 % deacreased in denominator i.e 9y/10
\frac{6x/5}{9y/10} = 16/21
So x/y = 4/7
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