Percentage Questions and Answers

Answer: C

The BMI changes by about minus 9%.

Mass is multiplied by 1.1, and height by 1.1, so the square of the height is multiplied by 1.21:

\[ \begin{aligned} \text{new BMI} &= \frac{1.1\,m}{(1.1\,h)^2} \\ &= \frac{1}{1.1} \times \frac{m}{h^2} \\ &\approx 0.909 \times \text{BMI} \end{aligned} \]

That is a fall of about 9.1%.

'Plus 10%' and 'Plus 11%' forget that height enters the formula squared, so the larger denominator wins. 'Minus 10%' treats division by 1.1 as subtracting 10%, but dividing by 1.1 lowers a value by only about 9.1%.

Answer: B

The answer is Suresh's land is more than Ramesh.

Ramesh acquires 10% of Suresh's 100 square yards, 10 square yards, so Ramesh has 110 and Suresh 90. Later Ramesh sells back 10% of his total plot of 110, which is 11 square yards:

\[ \begin{aligned} \text{Ramesh} &= 110 - 11 = 99 \\ \text{Suresh} &= 90 + 11 = 101 \end{aligned} \]

Suresh ends with 101 square yards and Ramesh with 99, so Suresh has more. They are not equal because 10% of 110 is more than the 10 that changed hands first.

Answer: C

The original fraction was \(\frac{4}{5}\).

Increasing by 300% multiplies the numerator by 4, and increasing by 400% multiplies the denominator by 5. If the fraction was \(\frac{x}{y}\):

\[ \begin{aligned} \frac{4x}{5y} &= \frac{16}{25} \\ \frac{x}{y} &= \frac{16}{25} \times \frac{5}{4} = \frac{4}{5} \end{aligned} \]

Check: \(\frac{4 \times 4}{5 \times 5} = \frac{16}{25}\). The common slip is to multiply by 3 and 4 instead of 4 and 5, which treats a 300% increase as tripling.

Answer: D

The original number is 800.

Decreasing by 20% and then increasing by 15% multiplies the number by \(0.8 \times 1.15 = 0.92\). The result is 8% less than the original, and that 8% equals 64:

\[ 0.08N = 64 \Rightarrow N = 800 \]

Check: 800 falls to 640, then rises to 736, which is 64 less than 800. 850, 750 and 700 give differences of 68, 60 and 56.

Answer: C

The answer is 16%.

To turn a fraction into a percentage, multiply by 100:

\[ \frac{4}{25} \times 100 = 4 \times 4 = 16\% \]

A quick check: 25 parts out of 100 is a quarter, so 4 parts out of 25 is the same as 16 parts out of 100.

40% and 24% do not follow from the fraction, and 4% is what you get by reading the numerator alone as a percentage.

Answer: C

The new price is ₹ 450.

A 10% reduction on ₹ 500 is

\[ \begin{aligned} \frac{10}{100} \times 500 &= 50 \\ 500 - 50 &= 450 \end{aligned} \]

Equivalently, the new price is 90% of the old: 0.9 × 500 = 450.

₹ 550 is the result of increasing the price by 10% instead of reducing it, ₹ 510 adds only ₹ 10, and ₹ 400 takes off 20%.

Answer: D

The original price is 250 rupees. A 12 % fall leaves 0.88 of the price, a 15 % fall leaves 0.85, and a 25 % rise multiplies by 1.25. \[0.88 \times 0.85 \times 1.25 = 0.935\] So the final price is 0.935 of the original price. Then \[P = \frac{233.75}{0.935} = 250\] Check: 250 x 0.88 = 220, 220 x 0.85 = 187, 187 x 1.25 = 233.75. The options 200, 225 and 240 give 187, 210.4 and 224.4, which do not match.

Answer: A

From the first condition, 30 per cent of A equals 50 per cent of B.

\[ 0.3A = 0.5B \Rightarrow B = \frac{0.3}{0.5}A = 0.6A \]

So B is 60 per cent of A, and since \(B = x\%\) of A, \(x = 60\). The value 160 is what you get if you express A as a percentage of B in the wrong direction (A = 1.67B would be about 167 per cent), and 80 and 90 do not follow from the equation. The answer is 60, option A.

Answer: C

The original number is 80. Let the number be x. Increased by 25 per cent it becomes 1.25x, and decreased by 30 per cent it becomes 0.70x. The difference is \[1.25x - 0.70x = 0.55x = 44\] so x = 80. Check: 1.25 x 80 = 100 and 0.7 x 80 = 56, and 100 - 56 = 44. The other options give differences of 44.28 for 80.50 and 41.5 for 75.50, and 37.4 for 68, none of which equals 44. Taking the original price as 100, three changes give 100 x 0.88 x 0.85 x 1.25 = 93.5, so the final price is 93.5 per cent of the original. Dividing 233.75 by 0.935 yields 250. This is why the answers 200, 225 and 240 fail.

Answer: C

20 per cent of the garden will be mowed in one hour. If the whole garden takes 5 hours, then in one hour 1/5 of the work is done, and \[\frac{1}{5} \times 100 = 20\] per cent. The options 15, 18 and 21 per cent would need the work to take about 6.7, 5.6 or 4.8 hours. Dividing 100 per cent by 5 hours gives the share per hour, 20 per cent. If it were 15, 18 or 21 per cent per hour, the garden would take about 6.67, 5.56 or 4.76 hours, and the question says it takes exactly five, so only 20 per cent fits.