The length of a rectangle is increased by 60%. By what percent would the width have to be decreased to maintain the same area ?

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RRB ASSISTANT LOCO PILOT (Patna) 2013 click here to view all questions

The length of a rectangle is increased by 60%. By what percent would the width have to be decreased to maintain the same area ?

A37(1 / 2)%

B0.6

C0.75

DNone

rahul ? Jan 15 '2020 at 9:30

Correct answer is: \(37 \frac{1}{2} \%\)

Explanation:

Let original length = x and
original breadth = y.
Then, original area = xy

New length =\( \frac{160x}{100} = \frac{8x}{5}\).
Let new breadth = zThen. \(\frac{8x}{5} \times z = xy => z = \frac{5y}{8}\)
\therefore Decrease in breadth = \(\Big(\frac{3y}{8} \times \frac{1}{y} \times 100 \Big) \% = 37\frac{1}{2}\% \)

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Correct answer is: \(37 \frac{1}{2} \%\) Explanation: Let original length = x and original breadth = y. Then, original area = xy New length =\( \frac{160x}{100} = \frac{8x}{5}\). Let new breadth = zThen. \(\frac{8x}{5} \times z = xy => z = \frac{5y}{8}\) \therefore Decrease in breadth = \(\Big(\frac{3y}{8} \times \frac{1}{y} \times 100 \Big) \% = 37\frac{1}{2}\% \) rahul ? answered Jan 15 '2020 at 9:30 All Comments

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