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Percentage Questions and Answers

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71.

In a certain school, 20 % of students are below 8 years of age. The number of students above 8 years of age is\(\frac{2}{3}\)  of the number of students of 8 years of age which is 48. What is the total number of students in the school?

Answer: D

Let the number of students be \(x\). 

Then, Number of students above 8 years of age \(= (100 -20)\)% of \(x = 80\)% of \(x\)

\(\therefore 80\)% of  \(x = 40 + \frac{2}{3} \) of 48

\(\Rightarrow \frac{80}{100}x = 80\)

\(\Rightarrow x = 100.\)

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72.

The population of a town increased from \(1,75,000\) to \(2,62,500 \) in a decade. The average percent increase of population per year is:

Answer: B

Increase in \(10\) years \(= (262500 - 175000) = 87500.\)

Increase % \(= (\frac{87500}{175000} \times 100)\) % \(= 50\) %

\(\therefore\) Required average \(= (\frac{50}{10})\) % \(= 5\) %

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73.

A fruit seller had some apples. He sells 40 % apples and still has 420 apples. Originally, he had:

Answer: D

Suppose originally he had \(x\) apples.

Then, \((100 - 40)\)% of \(x = 420\)

\(\Rightarrow \frac{60}{100} \times x = 420 \)

\(\Rightarrow x = (\frac{420 \times 100}{60}) = 700\)

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74.

Two numbers \(A\) and \(B\) are such that the sum of 5 % of \(A\) and 4 % of \(B \) is two-third of the sum of 6 % of \(A\) and 8 % of \(B. \) Find the ratio of \(A:B\)

Answer: D

5 % of \(A\) + 4% of \(B\) \(= \frac{2}{3}\) (6% of \(A + 8\)% of \(B\))

\(\Rightarrow \frac{5}{100}A + \frac{4}{100}B = \frac{2}{3}(\frac{6}{100}A + \frac{8}{100}B)\)

\(\Rightarrow \frac{1}{20}A + \frac{1}{25}B = \frac{1}{25}A + \frac{4}{75}B\)

\(\Rightarrow (\frac{1}{20} - \frac{1}{25})A = (\frac{4}{75} - \frac{1}{25})B\)

\(\Rightarrow \frac{1}{100}A = \frac{1}{75}B\)

\(\frac{A}{B} = \frac{100}{75} = \frac{4}{3}\)

\(\therefore Required ratio = 4: 3\)

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75.

A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percentage of his total score did he make by running between the wickets?

Answer: B

Number of runs made by running \(= 110 - (3 \times 4 + 8 \times 6) \)

\(= 100 - (60) \)

\(= 50.\)

\(\therefore\) Required percentage \(= (\frac{50}{110} \times 100)\)% \(= 45\frac{5}{11}\)%

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76.

A man spends 59% of his income and saves the rest.  What percentage of his expenditure does he save?

Answer: D

Total income of man = Rs. \(100x\)

Amount spend \(= \frac{59}{100} \times 100x = 59x\) (Rs.)

\(\Rightarrow \) Money saved \(= 100x - 59x = 41x\)

\(\therefore\) Percentage of his expenditure that he saves \(= \frac{41x}{59x} \times 100 = 69.49 \) %

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77.

Priya went to the stationers and bought things worth \(Rs. 25\), out of which \(30\)  paisa went on sales tax on taxable purchases. If the tax rate was \(6\) %, then what the cost of the tax free items?

Answer: C

The amount taxable purchases be \(Rs. x.\)

Then, \(6\) % of \(x = \frac{30}{100}\)

\(\Rightarrow x = (\frac{30}{100} \times \frac{100}{6}) = 5.\)

\(\therefore\) Cost tax free items \(= Rs. [25 - (5 + 0.30)] = Rs. 19.70\)

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78.

Ayan buys good worth \(Rs. 6650.\) He gets a rebate of \(6\) % on it. After getting the rebate, he pays sales tax \(10\) %. Find the amount he will have to pay for the goods.

Answer: A

Rebate \(= 6\) % of \(Rs. 6650 = Rs. (\frac{6}{100} \times 6650) = Rs. 399.\)

Sales tax \(= 10\) % of \(Rs. (6650 - 399) = Rs. (\frac{10}{100} \times 6251) = Rs. 625.10\)

\(\therefore\) Final amount \(= Rs. (6251 + 625.10) = Rs. 6876.10.\)

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79.

The marked price of a shirt is Rs 1280. If the shirt is being sold for Rs 900, then
what is the discount percentage?

Answer: C

Marked price \(= Rs. 1280\)

Selling price \(= Rs. 900\)

⇒ Discount % \(= \frac{1280-900}{1280} \times 100 \)

\(= \frac{380}{12.8} \)

\(= 29.68\)

 

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80.

A student multiplied a number by \(\frac{3}{5}\) instead of \(\frac{5}{3}.\) What is the percentage error in the calculation?

Answer: D

Let the number be \(x.\)

Then, error \(= \frac{5}{3}x - \frac{3}{5}x = \frac{16}{15}x.\)

Error % \(= (\frac{16x}{15} \times \frac{3}{5x} \times 100)\)% \(= 64\)%

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