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Percentage Questions and Answers

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111.

A man spends 75% of his income. His income increases by 20% and his
expenditure also increases by 10%. The percentage of increase in his savings is

Answer: C

The income of person be Rs \(y\)

So his expenditure be 75% of income which is \(= 0.75y\)

Saving \(= y- 0.75y = 0.25​​​​​​​y\)

Now after increment of 20 % in income the new income becomes \(= 1.2y\)

Given that bew expenditure is 10% more than previous one.So , new expenditure is \(= 1.1 \times 0.75y = 0.825y\)

New savings \(= 1.2y - 0.825y = 0.375y\)

Percentage increase in savings \(= \frac{0.375y-0.25y}{0.25y} \times 100 = 50%\)

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112.

If 20 % of \(a = b\), then \(b\) % of 20 is the same as:

Answer: A

20 % of \(a = b \Rightarrow \frac{20}{100}a = b.\)

\(\therefore b\) % of \(20 = (\frac{b}{100} \times 20) = (\frac{20}{100}a \times \frac{1}{100} \times 20) = \frac{4}{100}a = 4\)% of \(a\)

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113.

The ratio of the number of boys and girls in a school is 2 : 3. If 25% of the boys
and 30% of the girls are scholarship holders, the percentage of the school students who are
not scholarship holders is

Answer: A

 The number of boys be 2y and number of girls be 3y

25 % of boys \(= 0.25 \times 2y = 0.5y\)

30 % of girls \(= 0.3 \times 3y = 0.9y\)

total scholarship holder \(= 0.5y +0.9y = 1.4y\)

% of no scholership holder \(= \frac{3.6y}{5y} \times 100 = 72\)

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114.

The costs of daily ticket of local train is Rs 130 and Monthly Pass costs Rs
3091.40. If I buy the Monthly Pass and travel for 29 days in a month than I save (in
percentage)?

Answer: B

Train ticket cost for 1 day = Rs. 130

⇒ Cost for 29 days \(= 29 \times \times 130 = Rs.3770\)

Cost of monthly pass = Rs. 3091.40

⇒ Money saved = 3770 - 3091.40 = Rs. 678.6

\(\therefore\) Required % \(= \frac{678.6}{3770} \times 100 = 18\)

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115.

What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?

Answer: C

Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.

Number of such number =14

Therefore, Required percentage \(=(\frac{14}{70} \times 100)\)% \(= 20\)%

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116.

The weights of two iron balls are 3.5 kg and 7.5 kg. What is the percentage
weight of the 1st ball with respect to 2nd ball. 

Answer: A

Weight of 1st ball \(= 3.5 kg\) and weight of second ball \(= 7.5 kg\)

⇒ Percentage weight of the 1st ball with respect to 2nd ball

\(= \frac{3.5}{7.5} \times 100 \)

\(= \frac{35}{3} \times 4 = \frac{140}{3} \)

\(= 46\frac{2}{3}\)

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117.

The percentage increase in the area of a rectangle, if each of its sides is
increased by 20% is equal to

Answer: D

Let the length of rectangle be \(L\) units and breadth be \(B\) units.

So area of rectangle \(= L \times B\)

As both length and breadth has been increased by 20%

So new length = 1.2\(L\)

New breadth = 1.2\(B\)

New area \(= 1.2L \times 1.2B = 1.44LB\)

Percentage increase in area \(= \frac{1.44LB-LB}{LB} \times 100 = 44\)

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