Percentages Questions for SSC CHSL and MTS PDF

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Question 1: A girl spends 76% of her income. If her income increases by 18% and her expenditure increases by 25%,then what is the percentage increase or decrease in her savings (correct to one decimal place)?

a) 6.9%, decrease

b) 4.2%, decrease

c) 5.7%, increase

d) 8.4%, increase

1) Answer (B)

Solution:

Let the income of girl is 100

Expenditure is 76% of income

i.e, $\frac{76}{100}\times\ 100$

= 76

Saving = Income – expenditure

100 – 76 = 24

According to question,

income is increased by 18%

Increased income = $\frac{18}{100}\times\ 100\ +\ 100=118$

Expenditure is increased by 25%

increased expenditure = $\frac{25}{100}\times\ 76\ +\ 76=95$

New saving = 118 – 95 = 23

% decrease in saving = $\frac{\left(24-23\right)}{24}\times\ 100$

i.e; $4.16\ \simeq\ 4.2\ \%$

Hence, Option B is correct.

Question 2: The total number of students in a school is 1400, out of which 35% of the students are girls and the rest are boys. If 80% of the boys and 90% of the girls passed in an annual examination, then the percentage of the students who failed is:

a) 16.5

b) 21.5

c) 17.4

d) 15.8

2) Answer (A)

Solution:

Total number of students in a school is 1400.

35% of the students are girls and the rest are boys.

Number of girls = $\frac{35}{100}\times1400$ = 490

Number of boys = 1400 – 490 = 910

80% of the boys and 90% of the girls passed in an annual examination.

Number of students passed in the examination = $\frac{80}{100}\times910+\frac{90}{100}\times490$ = $728+441$ = 1169

Number of students failed in the examination = 1400 – 1169 = 231

Percentage of the students failed in the examination = $\frac{231}{1400}\times100$

= 16.5%

Hence, the correct answer is Option A

Question 3: Weight of A is 20% more than weight of B, whose weight is 30% more than weight of C. By how much percent weight of A is more than weight of C?

a) 44

b) 56

c) 69

d) 35.89

3) Answer (B)

Solution:

Weight of B is 30% more than weight of C.

B = $\frac{130}{100}\times$C

Weight of A is 20% more than weight of B.

A = $\frac{120}{100}\times$B = $\frac{120}{100}\times\frac{130}{100}\times$C = $\frac{156}{100}$C

Required percentage = $\frac{\frac{156}{100}C-C}{C}\times100$

= $\frac{56}{100}\times100$

= 56%

Hence, the correct answer is Option B

Question 4: A woman earns ₹ 1,000/day. After some weeks, she earns ₹1,160/day. By how much percentage did her earnings
increase?

a) 18%

b) 16%

c) 17%

d) 15%

4) Answer (B)

Solution:

Increase in earnings of the woman = 1160 – 1000 = ₹ 160/day

$\therefore\ $Percentage increase in earnings of the woman = $\frac{160}{1000}\times100=$ 16%

Hence, the correct answer is Option B

Question 5: Sachin’s income is 25% more than Dileep’s income. By how much percentage is Dileep’s income less than Sachin’s income ?

a) 15%

b) 20%

c) 18%

d) 22%

5) Answer (B)

Solution:

Let the income of Sachin = S

Income of Dileep = D

Given,  Sachin’s income is 25% more than Dileep’s income

$=$>  $\text{S}=\frac{125}{100}\text{D}$

$=$>  $\text{S}=\frac{5}{4}\text{D}$

$\therefore\ $Required Percentage = $\frac{S-D}{S}\times100$

= $\frac{\frac{5}{4}D-D}{\frac{5}{4}D}\times100$

= $\frac{\frac{D}{4}}{\frac{5D}{4}}\times100$

= $\frac{1}{5}\times100$

= 20%

$\therefore\ $Dileep’s income is 20% less than Sachin’s income

Hence, the correct answer is Option B

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Question 6: The volume of the water in two tanks, A and B,is in the ratio of 6 : 5. The volume of water in tank A is increased by 30%. By what percentage should the volume of water in tank B be increased so that both the tanks have the same volume of water?

a) 56%

b) 30%

c) 18%

d) 15%

6) Answer (A)

Solution:

Let the volume of water in tanks A and B are $6p$ and $5p$ respectively

Volume of water in tank A after increasing 30% = $\frac{130}{100}\times6p=7.8p$

Volume of water to be increased in tank B to have same volume as tank A = $7.8p-5p=2.8p$

$\therefore\ $Percentage increase in volume of water in tank B = $\frac{2.8p}{5p}\times100=56\%$

Hence, the correct answer is Option A

Question 7: Sachin scored 120 runs, which included 6 boundaries and 4 sixes. What percentage of his total score did he make by running between the wickets?

a) $45 %$

b) $46 \frac{4}{9} %$

c) $60 %$

d) $33 \frac{1}{3} %$

7) Answer (C)

Solution:

Total runs scored by Sachin =120

Runs scored in boundaries = $\left(6\times4\right)+\left(4\times6\right)=24+24=48$

Runs scored by running between wickets = $120-48=72$

$\therefore\ $Required Percentage = $\frac{72}{120}\times100=60\%$

Hence, the correct answer is Option C

Question 8: A and B spend 60% and 75% of their incomes, respectively. If the savings of A are 20% more than that of B. then by what percentage is the income of A less than the income of B?

a) 15

b) 20

c) 10

d) 25

8) Answer (D)

Solution:

Let the income of A and B be X and Y respectively.

Saving of A = X – $\frac{60}{100} \times$ X = 0.4X

Saving of B = Y – $\frac{75}{100} \times$ Y = 0.25Y

If the savings of A are 20% more than that of B then,

Saving of A = 0.25Y $\times \frac{120}{100} = 3Y/10

0.4X = 3Y/10

4X = 3Y

Ratio of income of A and B = 3 : 4

Required percentage = $\frac{(4 – 3)}{4} \times$ 100 = 25%

Question 9: The price of cooking oil increased by 25%. Find by how much percentage a family must reduce its consumption in order to maintain the same budget?

a) 70%

b) 80%

c) 30%

d) 20%

9) Answer (D)

Solution:

By the formula,

Decrements in the consumption in order to maintain the same budget = $\frac{increment in the rate}{100 + increment in the rate} \times 100$

= $\frac{25}{100 + 25} \times 100 = \frac{25}{125} \times 100 = 20%

Question 10: Sudha sold an article to Renu for ₹576 at a loss of 20%. Renu spent a sum of ₹224 on its transportation and sold it to Raghu at a price which would have given Sudha profit of 24%. The percentage of gain for Renu is:

a) 13.2%

b) 10.5%

c) 12.9%

d) 11.6%

10) Answer (D)

Solution:

Cost price for Sudha = $\frac{576}{80} \times$ 100 = 720

Cost price for Renu = 576

Final cost price for Renu = 576 + 224 = 800

Selling price for Renu = 24% profit of sudha

= 720 $ \times \frac{124}{100}$ = 892.8

Profit for Renu = 892.8 -800 = 92.8

The percentage of gain for Renu = $\frac{92.8}{800} \times$ 100 = 11.6%

Question 11: In an examination in which the full marks were 500, A scored 25% more marks than B, B scored 60% more marks than C and C scored 20% less marks than D. If A scored 80% marks, then the percentage of marks obtained by D is:

a) 65%

b) 60%

c) 50%

d) 54%

11) Answer (C)

Solution:

Given, Total marks = 500

A scored 80% marks in the examination

$\Rightarrow$  A = $\frac{80}{100}\times500$ = 400

A scored 25% more marks than B

$\Rightarrow$  A = $\frac{125}{100}$B

$\Rightarrow$  400 = $\frac{125}{100}$B

$\Rightarrow$  400 = $\frac{5}{4}$B

$\Rightarrow$  B = 320

B scored 60% more marks than C

$\Rightarrow$  B = $\frac{160}{100}$C

$\Rightarrow$  320 = $\frac{160}{100}$C

$\Rightarrow$  C = 200

C scored 20% less marks than D

$\Rightarrow$  C = $\frac{80}{100}$D

$\Rightarrow$  200 = $\frac{80}{100}$D

$\Rightarrow$  D = 250

$\therefore\ $Percentage of marks obtained by D = $\frac{250}{500}$ = 50%

Hence, the correct answer is Option C

Question 12: A, B and C donate 8%, 7% and 9%,of their salaries, respectively to a charitable trust. The salaries of A and B are same and the difference between their donations is ₹259. Thetotal donation of A and B is ₹1,185 more than that of C. The total donation ofA and C is what percentage ofthe total salaries of A, B and C? (Correct to one decimalplace)

a) 6.2%

b) 5.8%

c) 6.4%

d) 7.1%

12) Answer (B)

Solution:

Let the salaries of A, B and C be x, x, y.

Donation of A, B and C = 0.08x, 0.07x and 0.09z

Difference between donations of A and B = 259

0.08x – 0.07x = 259

x = 259/0.01 = 25900

Total donation of A and B = donation of A + 1185

0.08x + 0.07x = 0.09z + 1185

0.15x = 0.09z + 1185

0.09z = 0.15 $\times $ 25900 – 1185 = 2700

z = 2700/0.09 = 30000

Total donation of A and C = 0.08x + 0.09z

=0.08 $\times$ 25900 + 2700 = 2072 + 2700 = 4772

Total salaries of A, B and C = 25900 + 25900 +30000 = 81800

Required percentage = $\frac{4772}{81800} \times 100 = 5.8%

Question 13: Sonu saves 15% of her income. If her income increases by 20% and she still saves the same amount as before, then what is the percentage increase in her expenditure? (correct to one decimal place)

a) 23.5

b) 22.8

c) 23.8

d) 242

13) Answer (A)

Solution:

Let the initially income of Sonu be Rs.100.

saving = 15%

Expenditure = 100 – 15 = 85%

Saving = 100 -85 = Rs.15

Expenditure = 85% of 100 = Rs.85

Income after increment = 100 $\times \frac{120}{100}$ = Rs.120

Saving = 15

Expenditure = 120 – 15 = 105

Increment in expenditure = 105 – 85 = Rs.20

Percentage Increment in expenditure = $\frac{20}{85} \times$ 100 = 23.52%

Question 14: The population of town B is 300%more than that of town A.For the next two years. the population ofA increases by x% per year and that of B decreases by the same percentage per year. After 2 years, if the population of A and B become equal, then the value of x is ………

a) $30\frac{2}{3}$

b) $33\frac{1}{3}$

c) 40

d) 25

14) Answer (B)

Solution:

Let the population of town A be a.

Population of town B = $a + 300 \times \frac{300}{100} = 4a$

After the next 2 year –

a $\times (1+\frac{x}{100})^2 = 4a \times (1-\frac{x}{100})^2$

$(100+x)^2 = 4 \times (100 – x)^2$

100 + x = 2(100 – x)

3x = 100

x = 33$\frac{1}{3}$

Question 15: A person can save 25% of his income. If his income increases by 20% and still he saves the same amount as before, the percentage increase in his expenditure is ………..

a) $26\frac{2}{3}$

b) $24$

c) $25\frac{1}{3}$

d) $25$

15) Answer (A)

Solution:

Let the initially income of person be Rs.100.

Saving  = 100 $\times \frac{25}{100}$ = 25

expenditure = 100 -25 = 75

Final income = 100 $\times \frac{120}{100}$ = 120

Saving = 25

Expenditure = 120 – 25 = 95

Percentage increment in expenditure = $\frac{95 – 75}{75} \times 100 = 26\frac{2}{3}$

Question 16: In a test consisting of 120 questions, Anuradha answered 65% of thefirst 60 questions correctly. What percentage of the remaining questions does she need to answer correctly to score 75% in the test?

a) 80

b) 85

c) 84

d) 90

16) Answer (B)

Solution:

To score 75%, the total number of question need to be correct $=\dfrac{120\times 75}{100}=90$

In the first 60 questions, the corrected answer percentage $=\dfrac{60\times 65}{100}=39$

Hence, the remaining number of questions, need to be correct $=90-39=51$

Remaining questions, need to attempt $=60$

Hence, the corrected answer percentage should be $=\dfrac{51\times 100}{60}=85\%$

Question 17: A is 75% less than B and C is 75% of the difference between A and B. C is what percentage more than A?

a) 125

b) 100

c) 75

d) 90

17) Answer (A)

Solution:

As per the question,

Let B is = 100

So, as per the condition, A is 75% less than B, so A=25
As per the condition, c=$\dfrac{(A-B)\times 75}{100}=\dfrac{(100-25)\times 75}{100}=\dfrac{225}{4}$
Hence, the required percentage $=\dfrac{\dfrac{(225}{4}-25)\times 100}{25}=\dfrac{(225-100)\times 100}{100}=125$

Question 18: In an office, 70% of the total number of employees are females. 80% of the total number of employees, including 85 males, got promotion.If there are 105 female employees, then what percentage of female employees got promotion?

a) 40%

b) $33\frac{1}{3}\%$

c) 35%

d) 30%

18) Answer (B)

Solution:

105 female employee which is 70% of the total employee

so the total number of employee =$ 105 \times \dfrac{10}{7}$

$\Rightarrow 150 $

80% employee got a promotion so number of females who got a promotion = 120-85=35

so the %  of female employee got is  $\dfrac{35}{105}\times 100 $

$\Rightarrow 33 \dfrac{1}{3}$% Ans

Question 19: If A’s income is 40% of B’s income and B’s income is 24% more than C’s income, then by what percentage is C’s income more than A’s income? (Your answer should be correct to one decimal place.)

a) 75.6

b) 101.6

c) 104.2

d) 50.4

19) Answer (B)

Solution:

Let C income = 100

B’s income is 24% more than C

then B = 124

now A’s income is 40% of B income

so A income  = $ 124 \times \dfrac{40}{100} $

$\Rightarrow 49.6 $

so C’s income is 100- 49.6 = 50.4 (more than A)

then according to question $\dfrac{50.4}{49.6}\times 100 $

$\Rightarrow 101.6 $Ans

Question 20: If A is 48% more than B and C is 60%less than the sum of A and B, then A is what percentage more than C? (Correct to one decimalplace.)

a) 50.8

b) 49.2

c) 50.2

d) 49.8

20) Answer (B)

Solution:

Let B = 100 $x$

Here A =$ 148 x$

C = 60% less than A+B

= $\dfrac{40}{100} \times 248x $

$\Rightarrow \dfrac{992}{100}  x $

$\Rightarrow 99.2x $

Now A is more than C = $148x – 99.2x $

$\Rightarrow 48.8x$

% more than C = $\dfrac{48.2x}{99.2x}\times 100$

$\Rightarrow 49.19 $ %

$\Rightarrow 49.2$ % Ans

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