Percentage Questions and Answers

Q: In a class, 3/5 of the students are girls and rest are boys. If 2/9 of the girls and 1/4 of the boys are absent, then what part of the total number of students is present ?

The part present is \(\frac{23}{30}\).Girls are 3/5 of the class and boys 2/5. Of the girls, \(1 - \tfrac{2}{9} = \tfrac{7}{9}\) are present; of the boys, \(1 - \tfrac{1}{4} = \tfrac{3}{4}\):\[ \begin{aligned} \tfrac{3}{5} \times \tfrac{7}{9} + \tfrac{2}{5} \times \tfrac{3}{4} &= \tfrac{7}{15} + \tfrac{3}{10} \\ &= \tfrac{14}{30} + \tfrac{9}{30} = \tfrac{23}{30} \end{aligned} \]7/30 is the part absent, the complement of the answer. 17/25 and 18/49 do not arise from the given fractions.

Q: Two candidates, X and Y, contested an election. 100% of the voters cast their vote and there were no invalid votes. NOTA (None of The Above) option was not there. X got 20% of the votes cast and lost by 1623 votes. What is the total number of voters in the voters list?

The voters list has 2705 voters.Every voter voted, there were no invalid votes and no NOTA, so the votes cast equal the voters on the list, and Y received the other 80%.\[ \begin{aligned} 80\% - 20\% &= 60\% \text{ of } N = 1623 \\ N &= \frac{1623}{0.6} = 2705 \end{aligned} \]Check: X got 541 and Y got 2164, a margin of 1623. The larger options cannot be right: 60% of 6905 or of 12705 is far more than 1623.

Q: A scored 15 marks less than B in an examination. If B scored 25% more marks than A, then how much marks did B score?

B scored 75 marks.Let A score a. Then B = a + 15 and also B = 1.25a.\[ \begin{aligned} 1.25a &= a + 15 \\ 0.25a &= 15 \Rightarrow a = 60 \\ B &= 60 + 15 = 75 \end{aligned} \]Check: 75 is 25% more than 60. The option 60 is A's score, the usual trap. 35 and 40 do not satisfy both conditions: for B = 40, A would be 25, and 40 is 60% more than 25, not 25%.

Q: If the price of an article is decreased by 25%, and then the new price is increased by 45%, what is the net change (in %) in the price?

The net change is 8.75%, an increase.Successive percentage changes multiply, they do not add.\[ \begin{aligned} 0.75 \times 1.45 &= 1.0875 \\ \text{change} &= +8.75\% \end{aligned} \]The shortcut formula for changes x and y is \(x + y + xy/100 = -25 + 45 - 11.25 = 8.75\). −11.25 is only the cross term, 20 is the simple sum \(-25 + 45\), and −1.25 is a sign slip.

Q: Consider the following statements:1. If 48% of a number is 120, then 170% of the number will be 350.2. The number 3.5 can be expressed in terms of percentage as 350%,3. 1100 boys and 700 girls appeared in a test, 42% of the boys and 30% of the girls passed. The percentage of total who failed is \(62\frac{2}{3}\)%How many of the statements given above are correct?

Only two statements are correct.Statement 1: 48% of N is 120, so N = 250, and 170% of 250 is 425, not 350. False.Statement 2: 3.5 × 100% = 350%. True.Statement 3: passes are \(0.42 \times 1100 = 462\) boys and \(0.30 \times 700 = 210\) girls, 672 in all out of 1800, so 1128 failed.\[ \frac{1128}{1800} \times 100 = 62\tfrac{2}{3}\% \]True. So statements 2 and 3 are correct and statement 1 is not.

Q: There are 03 number of ways to reach from A to B and 04 number of ways to reach from B to C. What is the percentage of number of ways to reach A to B to the total number of ways to reach from A to C?

The percentage is 25%.Each of the 3 routes from A to B can be followed by any of the 4 routes from B to C, so the number of ways from A to C is the product:\[ \begin{aligned} A \to C &= 3 \times 4 = 12 \\ \frac{3}{12} \times 100 &= 25\% \end{aligned} \]300/7% (about 42.9%) comes from adding the routes (3 + 4 = 7) instead of multiplying them, the common error. 74% and 41% do not arise from the given numbers.

Q: The price of coffee increases by 20%. How much coffee can be bought now with the money which was sufficient to buy 10 kg of coffee previously?

About 8.33 kg can be bought now.Quantity bought with a fixed sum is inversely proportional to price. If the price rises by 20%, the new price is 1.2 times the old:\[ \frac{10}{1.2} = 8.33\ \text{kg} \]8 kg is the trap: it assumes a 20% price rise means 20% less coffee. In fact the quantity falls by 1/6, about 16.7%. 9 kg and 7.77 kg do not follow from the figures.

Q: Sudha secured 48% of Radha's marks, and Sunil secured 60% of Radha's marks. What is 'p' if Sudha secured 'p' percent of Sunil's marks?

Sudha secured 80 percent of Sunil's marks, so p = 80.Express both marks as fractions of Radha's marks R and divide.\[ \begin{aligned} \text{Sudha} &= 0.48R, \quad \text{Sunil} = 0.60R \\ p &= \frac{0.48R}{0.60R} \times 100 = 80 \end{aligned} \]Radha's marks cancel, so the answer does not depend on them. Taking the difference of the percentages (60 − 48 = 12) or reversing the ratio (60/48 = 125%) leads away from the options; 60 is simply Sunil's own percentage.

Q: A student who scored 30% marks in the first paper of Physics out of 180 marks, has to get an overall score of at least 50% in two papers. The second paper is of 150 marks. The percentage of marks he should score in the second paper to get the overall average score is __________ .

He must score 74% in the second paper.The two papers together carry 180 + 150 = 330 marks, and 50% of that is 165. In the first paper he scored 30% of 180:\[ \begin{aligned} 0.30 \times 180 &= 54 \\ 165 - 54 &= 111 \\ \frac{111}{150} \times 100 &= 74\% \end{aligned} \]So he needs 111 out of 150 in the second paper. A common slip is to average percentages, \(2 \times 50 - 30 = 70\%\), which ignores that the papers carry different maximum marks; that gives the 70% option.

Q: In an examination, it is required to get 36% of maximum marks to pass. A student gets 113 marks and is declared failed by 85 marks. The maximum marks is __________ .

The maximum marks are 550.The student scored 113 marks and fell short of the pass mark by 85, so the pass mark is \(113 + 85 = 198\). That is 36% of the maximum M:\[ \begin{aligned} 0.36\,M &= 198 \\ M &= \frac{198}{0.36} = 550 \end{aligned} \]Check: 36% of 550 is 198, and \(198 - 113 = 85\). Taking the 113 marks alone as 36% would give about 314, which is not offered, and 500, 640 and 1000 do not give a pass mark 85 above 113.

Important Instructions

31.

In a class, 3/5 of the students are girls and rest are boys. If 2/9 of the girls and 1/4 of the boys are absent, then what part of the total number of students is present ?

A.\(\frac{23}{30}\)
B.\(\frac{7}{30}\)
C.\(\frac{17}{25}\)
D.\(\frac{18}{49}\)

Exam Year(s)

HPPSC HPAS - 2025,

Answer: A

The part present is \(\frac{23}{30}\).

Girls are 3/5 of the class and boys 2/5. Of the girls, \(1 - \tfrac{2}{9} = \tfrac{7}{9}\) are present; of the boys, \(1 - \tfrac{1}{4} = \tfrac{3}{4}\):

\[ \begin{aligned} \tfrac{3}{5} \times \tfrac{7}{9} + \tfrac{2}{5} \times \tfrac{3}{4} &= \tfrac{7}{15} + \tfrac{3}{10} \\ &= \tfrac{14}{30} + \tfrac{9}{30} = \tfrac{23}{30} \end{aligned} \]

7/30 is the part absent, the complement of the answer. 17/25 and 18/49 do not arise from the given fractions.

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32.

Two candidates, X and Y, contested an election. 100% of the voters cast their vote and there were no invalid votes. NOTA (None of The Above) option was not there. X got 20% of the votes cast and lost by 1623 votes. What is the total number of voters in the voters list?

A.2705
B.6905
C.12605
D.12705

Exam Year(s)

Haryana Civil Services - 2026, HPSC - 2026,

Answer: A

The voters list has 2705 voters.

Every voter voted, there were no invalid votes and no NOTA, so the votes cast equal the voters on the list, and Y received the other 80%.

\[ \begin{aligned} 80\% - 20\% &= 60\% \text{ of } N = 1623 \\ N &= \frac{1623}{0.6} = 2705 \end{aligned} \]

Check: X got 541 and Y got 2164, a margin of 1623. The larger options cannot be right: 60% of 6905 or of 12705 is far more than 1623.

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33.

A scored 15 marks less than B in an examination. If B scored 25% more marks than A, then how much marks did B score?

A.35
B.40
C.60
D.75

Exam Year(s)

Haryana Civil Services - 2026, HPSC - 2026,

Answer: D

B scored 75 marks.

Let A score a. Then B = a + 15 and also B = 1.25a.

\[ \begin{aligned} 1.25a &= a + 15 \\ 0.25a &= 15 \Rightarrow a = 60 \\ B &= 60 + 15 = 75 \end{aligned} \]

Check: 75 is 25% more than 60. The option 60 is A's score, the usual trap. 35 and 40 do not satisfy both conditions: for B = 40, A would be 25, and 40 is 60% more than 25, not 25%.

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34.

If the price of an article is decreased by 25%, and then the new price is increased by 45%, what is the net change (in %) in the price?

A.−11.25
B.−1.25
C.8.75
D.20

Exam Year(s)

Haryana Civil Services - 2026, HPSC - 2026,

Answer: C

The net change is 8.75%, an increase.

Successive percentage changes multiply, they do not add.

\[ \begin{aligned} 0.75 \times 1.45 &= 1.0875 \\ \text{change} &= +8.75\% \end{aligned} \]

The shortcut formula for changes x and y is \(x + y + xy/100 = -25 + 45 - 11.25 = 8.75\). −11.25 is only the cross term, 20 is the simple sum \(-25 + 45\), and −1.25 is a sign slip.

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35.

Consider the following statements:

1. If 48% of a number is 120, then 170% of the number will be 350.
2. The number 3.5 can be expressed in terms of percentage as 350%,
3. 1100 boys and 700 girls appeared in a test, 42% of the boys and 30% of the girls passed. The percentage of total who failed is \(62\frac{2}{3}\)%

How many of the statements given above are correct?

A.Only one
B.Only two
C.All three
D.None

Exam Year(s)

Haryana Civil Services - 2026, HPSC - 2026,

Answer: B

Only two statements are correct.

Statement 1: 48% of N is 120, so N = 250, and 170% of 250 is 425, not 350. False.

Statement 2: 3.5 × 100% = 350%. True.

Statement 3: passes are \(0.42 \times 1100 = 462\) boys and \(0.30 \times 700 = 210\) girls, 672 in all out of 1800, so 1128 failed.

\[ \frac{1128}{1800} \times 100 = 62\tfrac{2}{3}\% \]

True. So statements 2 and 3 are correct and statement 1 is not.

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36.

There are 03 number of ways to reach from A to B and 04 number of ways to reach from B to C. What is the percentage of number of ways to reach A to B to the total number of ways to reach from A to C?

A.25%
B.74%
C.300/7%
D.41%

Exam Year(s)

ISRO Assistant - 2023,

Answer: A

The percentage is 25%.

Each of the 3 routes from A to B can be followed by any of the 4 routes from B to C, so the number of ways from A to C is the product:

\[ \begin{aligned} A \to C &= 3 \times 4 = 12 \\ \frac{3}{12} \times 100 &= 25\% \end{aligned} \]

300/7% (about 42.9%) comes from adding the routes (3 + 4 = 7) instead of multiplying them, the common error. 74% and 41% do not arise from the given numbers.

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37.

The price of coffee increases by 20%. How much coffee can be bought now with the money which was sufficient to buy 10 kg of coffee previously?

A.7.77 kg
B.8 kg
C.8.33 kg
D.9 kg

Exam Year(s)

ISRO Assistant - 2023,

Answer: C

About 8.33 kg can be bought now.

Quantity bought with a fixed sum is inversely proportional to price. If the price rises by 20%, the new price is 1.2 times the old:

\[ \frac{10}{1.2} = 8.33\ \text{kg} \]

8 kg is the trap: it assumes a 20% price rise means 20% less coffee. In fact the quantity falls by 1/6, about 16.7%. 9 kg and 7.77 kg do not follow from the figures.

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38.

Sudha secured 48% of Radha's marks, and Sunil secured 60% of Radha's marks. What is 'p' if Sudha secured 'p' percent of Sunil's marks?

A.50
B.60
C.70
D.80

Exam Year(s)

Kerala PSC KAS - 2020,

Answer: D

Sudha secured 80 percent of Sunil's marks, so p = 80.

Express both marks as fractions of Radha's marks R and divide.

\[ \begin{aligned} \text{Sudha} &= 0.48R, \quad \text{Sunil} = 0.60R \\ p &= \frac{0.48R}{0.60R} \times 100 = 80 \end{aligned} \]

Radha's marks cancel, so the answer does not depend on them. Taking the difference of the percentages (60 − 48 = 12) or reversing the ratio (60/48 = 125%) leads away from the options; 60 is simply Sunil's own percentage.

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39.

A student who scored 30% marks in the first paper of Physics out of 180 marks, has to get an overall score of at least 50% in two papers. The second paper is of 150 marks. The percentage of marks he should score in the second paper to get the overall average score is __________ .

A.80%
B.76%
C.74%
D.70%

Exam Year(s)

KPSC KAS - 2020,

Answer: C

He must score 74% in the second paper.

The two papers together carry 180 + 150 = 330 marks, and 50% of that is 165. In the first paper he scored 30% of 180:

\[ \begin{aligned} 0.30 \times 180 &= 54 \\ 165 - 54 &= 111 \\ \frac{111}{150} \times 100 &= 74\% \end{aligned} \]

So he needs 111 out of 150 in the second paper. A common slip is to average percentages, \(2 \times 50 - 30 = 70\%\), which ignores that the papers carry different maximum marks; that gives the 70% option.

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40.

In an examination, it is required to get 36% of maximum marks to pass. A student gets 113 marks and is declared failed by 85 marks. The maximum marks is __________ .

A.500
B.550
C.640
D.1000

Exam Year(s)

KPSC KAS - 2020,

Answer: B

The maximum marks are 550.

The student scored 113 marks and fell short of the pass mark by 85, so the pass mark is \(113 + 85 = 198\). That is 36% of the maximum M:

\[ \begin{aligned} 0.36\,M &= 198 \\ M &= \frac{198}{0.36} = 550 \end{aligned} \]

Check: 36% of 550 is 198, and \(198 - 113 = 85\). Taking the 113 marks alone as 36% would give about 314, which is not offered, and 500, 640 and 1000 do not give a pass mark 85 above 113.

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