Ram and Shyam are climbing a tree. Ram weighs $50kg$ and Shyam weighs $60kg$ . Power expended by Ram and Shyam to climb the tree are in the ratio of $3:2$ . What is the ratio of time taken by Ram and Shyam to climb the tree?

18:10

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10:18

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5:18

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18:5

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Solution

The correct option is B
10:18

Let mass of Ram be $m_{1}$

mass of Shyam be $m_{2}$

power expended by Ram be $P_{1}$

power expended by Shyam be $P_{2}$

height of the tree be $h$

time taken by ram to climb the tree be $t_{1}$

time taken by Shyam to climb the tree be $t_{2}$

Work done = mgh
$P o w e r = \frac{w o r k}{t i m e}$
$\frac{P_{1}}{P_{2}}$ = $\frac{m_{1} g h t_{2}}{m_{2} g h t_{1}}$
$3 : 2 = \frac{50 t_{2}}{60 t_{1}}$
$\frac{t_{1}}{t_{2}} = 10 : 18 = 5 : 9$

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