Percentage Questions for SSC MTS

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Question 1: The average weight of the boys in a class is 69.3 kg and that of the girls in the same class is 59.4 kg. If the average weight of all the boys and girls in the class is 63.8 kg, then the percentage of the number of boys in the class is:

a) $55\frac{5}{9}$

b) 40

c) 45

d) $44\frac{4}{9}$

1) Answer (D)

Solution:

Let B be the number of Boys, G be number of girls

$ \dfrac {total   weight   of   boys}  {number  of   boys} $= Any weight of boys

total weight of boys = (69.3)B

Similarly total weight of girls = (59.4) G

total weight of class = 69.3 B + 59.4 G

Any weight of class = $\dfrac{total   weight   of   class}{total   Boys  + Girls} $

$\Rightarrow 63.8 = \dfrac{ 63.3 B + 59.4 G} {B + G} $

$\Rightarrow 63.8 B + 63.8 G = 69.3 B + 59.4 G $

$\Rightarrow 4.4 G = 5.5 B $

$\Rightarrow G = \dfrac {5}{4} B $

% of Boys in class = $\dfrac{B}{B+G} \times 100 $

$\Rightarrow \dfrac{B}{B + \dfrac{5}{4}B} \times 100 $

$\Rightarrow \dfrac{B}{B+ \dfrac{9}{4}B} \times 100 $

$\Rightarrow \dfrac{4}{9} \times 100 $

$\Rightarrow \dfrac {400}{9} $

$\Rightarrow 44 \dfrac{4}{9} $ Ans

Question 2: In a school, 60% of the numberof students are boys and the rest are girls. If 20% of the number of boys failed and 65% of the number of girls passed the examination, then the percentage of the total number of students who passed is:

a) 68

b) 72

c) 74

d) 78

2) Answer (C)

Solution:

Let total number of students in school = 100

=> Number of boys = 60 and number of girls = 40

Boys who passed = $\frac{80}{100}\times60=48$

Girls who passed = $\frac{65}{100}\times40=26$

$\therefore$ Total percentage of students passed = $48+26=74\%$

=> Ans – (C)

Question 3: A man spends $\frac{2}{3}rd$ of his income. If his income increases by 14% and the expenditure increases by 20%, then the percentage increase in his savings will be

a) 1%

b) 2%

c) 4%

d) 6%

3) Answer (B)

Solution:

Let initial income be Rs. 300

=> Expenditure = Rs. 200 and savings = Rs. 100

Now, new income after 14% increase = $\frac{114}{100}\times300=Rs.$ $342$

Similarly, new expenditure = Rs. 240

=> New savings = Rs. $(342-240)=Rs.$ $102$

$\therefore$ Increase in savings = $\frac{(102-100)}{100}\times100=2\%$

=> Ans – (B)

Question 4: A is 40% less than B, and C is 40% of the sum of A and B. The difference between A and B is what percentage of C?

a) 60.5%

b) 64%

c) 62.5%

d) 60%

4) Answer (C)

Solution:

Let $B = 10$, => $A = 6$

=> $C = \frac{40}{100}\times(10+6)=6.4$

$\therefore$ Required % = $\frac{(B-A)}{C}\times100$

= $\frac{4}{6.4}\times100=62.5\%$

=> Ans – (C)

Question 5: The monthly salary of a person was ₹50,000. He used to spend on three heads- personal and family expenses (E), taxes (T), philanthropy (P), and rest were his savings. E was 50% of the income, T was 20% of E and P was 15% of T. When his salary got raised by 40%, he maintained the percentage level of E, but T became 30% of E and P became 20% of T. By whatpercentage is the new savings more or less than the earlier savings? (correct up to one decimal place)

a) 16.4% more

b) 8.2% more

c) 16.4% less

d) 8.2% less

5) Answer (A)

Solution:

Initial salary of person = Rs. 50,000

Total % expenditure = $50+(\frac{20}{100}\times50)+(\frac{15}{100}\times\frac{20}{100}\times50)$

= $50+10+1.5=61.5\%$

=> % savings initially = $100-61.5=38.5\%$

Total savings = $\frac{38.5}{100}\times50,000=Rs.$ $19,250$

Now, new salary = Rs. 70,000

Similarly, total % expenditure = $50+(\frac{30}{100}\times50)+(\frac{20}{100}\times\frac{30}{100}\times50)$

= $50+15+3=68\%$

=> % savings initially = $100-68=32\%$

Total savings = $\frac{32}{100}\times70,000=Rs.$ $22,400$

$\therefore$ New savings are more by = $\frac{22400-19250}{19250}\times100\approx16.4\%$

=> Ans – (A)

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Question 6: If the word PHOTOGRAPH is spelt with ‘F’ in place of ‘PH’, then what would bethe percentage reduction in the number of letters?

a) 25%

b) 10%

c) 20%

d) 18%

6) Answer (C)

Solution:

Number of letters in PHOTOGRAPH = 10

Number of letters in FOTOGRAF = 8

=> % reduction = $\frac{10-8}{10}\times100=20\%$

=> Ans – (C)

Question 7: In a class, $83\frac{1}{3}\%$ of the number of studentsare girls and the rest are boys. If 60% of the number of boys and 80% of the number of girls are present, then what percentage of the total number of students in the class is absent?

a) 26$\frac{2}{3}$

b) 22$\frac{2}{3}$

c) 23$\frac{1}{3}$

d) 12$\frac{1}{3}$

7) Answer (C)

Solution:

Let the total students be x.
Girls = $83\frac{1}{3}\%x = \frac{250x}{300} = \frac{5x}{6}$
Boys = x – $\frac{5x}{6} = \frac{x}{6}$
Absent boys = (100% – 60% = 40%) of the number of boys
= $\frac{x}{6} \times \frac{40}{100} = \frac{x}{15}$
Absent girls = (100% – 80% = 20%) of the number of girlss
= $\frac{5x}{6} \times \frac{20}{100} = \frac{x}{6}$
Absent students =$\frac{x}{15} + \frac{x}{6} = \frac{7x}{30}$
Percentage absent students = $\frac{\frac{7x}{30}}{x} \times 100  = 23 \frac{1}{3}$

Question 8: Raghav spends 80% of his income. If his income increases by 12% and the savings decrease by 10%, then what will be the percentage increase in his expenditure?

a) 20.5

b) 16

c) 17.5

d) 22

8) Answer (C)

Solution:

Let the income of Raghav be Rs.100.
Expenditure = 80
Saving = Rs.20
Income increases by 12% and the savings decrease by 10%,
So, income = 112,
Saving = 20 $\times \frac{90}{100} = 18$
Expenditure = 112 – 18 = 94
Increment in his expenditure = 94 – 80 = 14
Percentage increment in expenditure = $\frac{14}{80} \times 100 = 20$

Question 9: In an examination, 40% of the students who appeared were boys and the rest were girls. The pass percentage of the boys was 60% and the overall pass percentage was 56%. What was the pass percentage of the girls?

a) 54$\frac{2}{3}$

b) 54$\frac{1}{3}$

c) 52$\frac{2}{3}$

d) 53$\frac{1}{3}$

9) Answer (D)

Solution:

Let’s assume the total number of students who appeared on the exam are 100.

boys appeared the exam = 40% of 100 = 40

girls appeared the exam = (100-40) = 60

boys who appeared and passed the exam = 60% of 40 = 24

overall students who appeared and passed the exam = 56% of 100 = 56

girls who appeared and passed the exam = 56-24 = 32

the pass percentage of the girls = $\frac{32\ \times\ 100}{60}$ = 53$\frac{1}{3}$

therefore answer is option D

Question 10: Daily ticket of a metro train costs ₹120 and Monthly pass costs ₹3276. If Sohan buys the Monthly pass and travels for 30 days in a month then what Percentage does he save?

a) 18%

b) 15%

c) 12%

d) 9%

10) Answer (D)

Solution:

ticket cost per day is 120

if the man travels for 30 days,the cost would be 120$\times\ $30=3600

Given that monthly pass costs 3276

therefore the percentage of amount he saves is $\frac{(3600-3276)}{3600}\times100$

= $\frac{324}{3600}\times100$

9% is the correct answer.

Question 11: A box contains 780 bananas out of which 130 bananas are rotten and rest are of good quality. The percentage (correct to two decimal places) of good quality of bananas is:

a) 71.12%

b) 53.33%

c) 65.35%

d) 83.33%

11) Answer (D)

Solution:

Out of 780 bananas, 130 are rotten means the remaining are 780-130=650

percentage of good quality bananas is $\frac{650}{780}\times100$=83.33%

hence answer is option D

Question 12: In spite of an increase in the price of a commodity by 20%, the overall expenditure on it increases by 12%. What is the percentage decrease in the quantity of commodities consumed?

a) $7\frac{1}{3}$

b) $7\frac{1}{2}$

c) 8

d) $6\frac{2}{3}$

12) Answer (D)

Solution:

Let’s assume the number of commodities consumed initially is 10 and the price of each commodity is 10.

Total expenditure initially = $10\times10$ = 100

In spite of an increase in the price of a commodity by 20%, the overall expenditure on it increases by 12%.

Price of each commodity after increase = 10 of (100+20)%

= 10 of 120%

= 12

Total expenditure after the increase in the price = 100 of (100+12)%

= 100 of 112%

= 112

number of commodities consumed after the increase in the price = $\frac{112}{12}$

= $\frac{28}{3}$

Percentage decrease in the quantity of commodities consumed = $\frac{\left(10-\frac{28}{3}\right)}{10}\times\ 100$

= $\frac{\left(\frac{30}{3}-\frac{28}{3}\right)}{10}\times\ 100$

= $\frac{\frac{2}{3}}{10}\times\ 100$

= $\frac{2}{30}\times\ 100$

= $\frac{20}{3}$

= $6\frac{2}{3}$ %

Question 13: In an examination, the average score of students in a class who passed is 69 and that of those who failed is 61. If the average score of all the students, who appeared in the examination is 66, then the percentage of students who passed is:

a) 37.5

b) 60

c) 62.5

d) 56

13) Answer (C)

Solution:

Let’s assume the number of students who passed and failed the exam are P and F respectively.

69P+61F = 66(P+F)

69P+61F = 66P+66F

69P-66P = 66F-61F

3P = 5F

P : F = 5 : 3

Percentage of students who passed = $\frac{5}{5+3}\times\ 100$

= $\frac{5}{8}\times\ 100$

= 62.5%

Question 14: In an examination, there are 800 boys and 600 girls. 40% boys and 60% girls passed the examination. The percentage (correct to two decimal places) of failed students from the total students is:

a) 52.34%

b) 50.36%

c) 51.43%

d) 53.57%

14) Answer (C)

Solution:

given there are 800 boys

40%of boys passed examination

i.e; $800\times\frac{40}{100}$ =320 boys passed exam

Given that there are 600 girls and 60% of girls passed exam

i.e; $600\times\frac{60}{100}$=360 girls

total number of passed students = 360+320=680

so no of failed students= 800+600-680

=720

so percentage of failed students = $\frac{720\ \times\ 100}{1400}$

51.42%

hence answer is option C

Question 15: Manish’s salary is half of Ravi’s salary. Ravi’s salary is how much percentage more than Manish’s Salary?

a) 100%

b) 25%

c) 50%

d) 75%

15) Answer (A)

Solution:

Lets Ravi salary = 2x

And , Manish salary = x

Therefore,

percentage more = $\frac{\left(2x-x\right)}{x}\times\ 100$

= $\frac{x}{x}\times\ 100$

= 100%

Question 16: If the selling price of an article is 25% of its cost price, then what will be the loss percentage?

a) 25%

b) 60%

c) 75%

d) 50%

16) Answer (C)

Solution:

Let the CP of the article be 100.

According to the question, SP of the article is 25 % of CP of the article , i.e. SP= 25

Hence, Loss = CP-SP = 100-25 = 75

Loss % = $\frac{75\ \times\ 100}{100}$ = 75 %.

Question 17: A number is first increased by 40% and then it is increased by 30%. What is the net percentage increase?

a) 82%

b) 96%

c) 72%

d) 70%

17) Answer (A)

Solution:

Let the number be 100

So when it is increased by 40 % then it becomes = 140.

Again it is increased by 30 % then it becomes = 30 % of 140 + 140 = 42 + 140 = 182

Hence, the net percentage change in the number is $\frac{182-100}{100}$= 82 %.

Question 18: Side of a square is first increased by 10% and then decreased by 20%. What is the overall percentage change in area?

a) Increase by 18.24%

b) Decrease by 22.56%

c) Decrease by 18.24%

d) Increase by 22.56%

18) Answer (B)

Solution:

Let the side of the square be 100

side increased by 10%

then S1 = $ 100 +( \frac{10}{100} \times 100 ) $

= 110

The resultant side then decreased by 20%

S2 = $ 110 – ( \frac{20}{100} \times 110 ) $

= 88

A1 = $ S1^2 $

= 12100

A2 = $ S2^2 $

= 7744

A2 < A1. That means the area is decreased from initially. Hence the change will also be a decrease.

overall percentage change in area = $ \frac{10000 – 7744}{10000} \times 100 $

= 22.56%

Question 19: If A is 200% more than B, then B is how much percentage less than A?

a) 33.33%

b) 50%

c) 100%

d) 66.67%

19) Answer (D)

Solution:

Let B = 100.

A is 200% more than B. Therefore $B\times\frac{100 + 200}{100} = A$

$100\times\frac{300}{100} = 300$

therefore A = 300.

To find how much percent B less than A,

$300\times\frac{100 – x}{100} = 100$

$100 – x = \frac{100}{3}$

$x = 100 – \frac{100}{3}$

$x = \frac{200}{3}$

$x = 66.67$

hence B is 66.67% less than A.

Question 20: 320 is how much percentage less than 400?

a) 20%

b) 18%

c) 12%

d) 15%

20) Answer (A)

Solution:

= $\frac{\left(400-320\right)}{400}\times\ 100$

= $\frac{\left(80\right)}{400}\times\ 100$

20%

hence answer is option a

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