MCQ on Percentage Questions and Solutions, Explanations

MCQ on Percentage for competitive exams like Bank PO/Clerk, SBI PO, SBI Clerk, IBPS PO, IBPS Clerk, IBPS RRB, RBI, SSC, SSC CGL, SSC CHSL, SSC MTS, SSC GD, RRB NTPC, RRB Group D, Insurance, AFCAT, CDS, CLAT, CAPF, and NDA.

MCQ on Percentages for competitive Exams

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Solve the following questions on percentages.

If the numerator of certain fraction is increased by 200% and the denominator is increased by 150% the new fraction thus formed is \(\displaystyle \frac{9}{{10}}\) .What is the original fraction ?

(a) \(\displaystyle \frac{3}{4}\)

(b) \(\displaystyle \frac{1}{4}\)

(d) \(\displaystyle \frac{2}{5}\)

(e) None of these

Solution: (a)

Let the original fraction be =\(\displaystyle \frac{x}{y}\)

Therefore, \(\displaystyle \frac{{x\times 300}}{{y\times 250}}=\frac{9}{{10}}\)

\(\displaystyle \Rightarrow \) \(\displaystyle \frac{{x\times 6}}{{y\times 5}}=\frac{9}{{10}}\)

\(\displaystyle \Rightarrow \) \(\displaystyle \frac{x}{y}=\frac{9}{{10}}\times \frac{5}{6}=\frac{3}{4}\)

If the numerator of a certain fractions increased by 100% and the denominator is increased by 200%; the new fraction thus formed is \(\displaystyle \frac{4}{{21}}\) What is the original fraction ?

(a) \(\displaystyle \frac{2}{7}\)

(b) \(\displaystyle \frac{3}{7}\)

(d) \(\displaystyle \frac{4}{7}\)

(e) None of these

Solution: (a)

Let the original fraction be = \(\displaystyle \frac{x}{y}\)

\(\displaystyle \Rightarrow \) \(\displaystyle \frac{{x\times 200}}{{y\times 300}}=\frac{4}{{21}} \)

\(\displaystyle \Rightarrow \)\(\displaystyle \frac{x}{y}=\frac{4}{{21}}\times \frac{3}{2}=\frac{2}{7}\)

The difference between 55% of a number and 14% of the same number is 8610. What is 85% of that number?

(a) 15850

(b) 17020

(d) 18450

(e) None of these

Solution: (a)

Let the number be x. Now, according to the question,

(55 – 14) % of x = 8610

\(\displaystyle \Rightarrow \)\(\displaystyle \frac{{x\times 41}}{{100}}=8610\)

\(\displaystyle \Rightarrow \)\(\displaystyle x=\frac{{8610\times 100}}{{41}}=2100\)

\(\displaystyle \Rightarrow \)\(\displaystyle \frac{{21000\times 85}}{{100}}\)=17850

Animesh got 102 marks in Hindi, 118 marks in Science, 104 marks in Sanskrit, 114 marks in Maths and 96 marks in English. The maximum marks of each subject are 120. How much overall percentage of marks did Animesh get?

(a) 82

(b) 89

(d) 72

(e) None of these

Solution: (b)

Total marks obtained by Animesh

= 102 + 118 + 104 + 114 + 96 = 534

Total maximum marks = 120 × 5 = 600 \ Required percentage= \(\displaystyle \frac{{534}}{{600}}\times 100\) =89

Madhur got 101 marks in Hindi, 100 marks in Science, 96 marks in Sanskrit, 108 marks in Maths and 78 marks in English. If the maximum marks of each subject is equal and if Madhur scored 84 per cent marks in all the subjects together, what is the maximum marks of each subject?

(a) 110

(b) 120

(d) 100

(e) None of these

Solution: (c)

Total marks = 101 + 100 + 96 + 108 + 78 = 483

Since it is 84% of the total maximum marks,

Let total maximum marks be x

\(\displaystyle \frac{{84}}{{100}}x=483\)

x=\(\displaystyle \frac{{483\times 100}}{{84}}=575\)

Maximum marks of each subject = \(\displaystyle \frac{{575}}{5}\) = 115

Alternate method,

If each paper is of “x” marks, then total marks=5x

Given, total marks = 101 + 100 + 96 + 108 + 78 = 483

Mathur scored 84% marks in total, (which is 484 marks)

483 marks —— 5x marks

84%————–100%

Cross-multiply

\(\displaystyle \begin{array}{l}5x\times 84=483\times 100\\5x=\frac{{483\times 100}}{{84}}=575\\x=115\end{array}\)

In an examination, the maximum aggregate marks that a student can get is 1040. In order to pass the exam, a student is required to get 676 marks out of the aggregate marks. Mina got 624 marks. By what percent did Mina fail in the exam?

(a) 5%

(b) 8%

(d) Cannot be determined

(e) None of these

Solution: (a)

Minal failed by (676 – 624) = 52 marks

% marks =\(\displaystyle \frac{{52}}{{1040}}\times 100=5\%\)

The product of 5% of a positive number and 2% of the same number is 211.6. What is half of that number?

(a) 230

(b) 460

(d) 115

(e) None of these

Solution: (a)

Let the number be x. Then, according to the question,

\(\displaystyle \frac{{5x}}{{100}}\times \frac{{2x}}{{100}}=211.6\)

or \(\displaystyle {{x}^{2}}=\frac{{211.6\times 100\times 100}}{{5\times 2}}=211600\)

x = + 460

Therefore, half of eight number = 230

Nandita scored 80% marks in five subjects together viz Hindi, Science, Maths, English and Sanskrit, where in the maximum marks of each subject were 105. How many marks did Nandita score in Science if she scored 89 marks in Hindi, 92 marks in Sanskrit, 98 marks in Maths and 81 marks in English?

(a) 60

(b) 75

(d) 70

(e) None of these

Solution: (a)

Total marks scored by Nandita =\(\displaystyle 525\times \frac{{80}}{{100}}=420\)

Let Score in Science be x

89 + 92 + 98 + 81 + x = 420

360 + x = 420

\(\displaystyle \Rightarrow \)x = 60

Niraj incurred a loss of 55 percent on selling an article for ₹ 9,549. What was the cost price of the article?

(a) ₹ 27,700

(b) ₹ 25,600

(d) ₹29,000

(e) None of these

Solution: (c)

Let cost Price of article be x

\(\displaystyle x-\frac{{55}}{{100}}x=9549\)

\(\displaystyle \frac{{45x}}{{100}}=9549\)

x=\(\displaystyle \frac{{9549\times 100}}{{45}}=21220\)

In order to pass in an exam, a student is required to get 780 marks out of the aggregate marks. Sonu got 728 marks and was declared failed by 5 percent. What are the maximum aggregate marks a student can get in the examination?

(a) 1040

(b) 1100

(d) Cannot be determined

(e) None of these

Solution: (a)

5% of maximum aggregate marks = 780 – 728 = 52

Let maximum aggregate marks be x

5% of x = 52

Maximum aggregate marks = \(\displaystyle \frac{{52}}{5}\times 100=1040\)

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Solve the following questions on percentages.

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