If 30% of A is added to 40% of B, the answar is 80% of B. What percentage of A is B?
Answer: D
\[ 0.30A + 0.40B = 0.80B \]
\[ 0.30A = 0.40B \quad\Longrightarrow\quad \frac{B}{A} = \frac{0.30}{0.40} = 0.75 \]
So B is 75% of A. Note the question asks for B as a percentage of A, not the other way round - that would be 133.3%.
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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 \(= y- 0.75y = 0.25y\)
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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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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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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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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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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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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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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