Q 11-05-107JEE MainJEE Main 2023 (13 Apr, Shift 1)Medium
The ratio of powers of two motors is $\dfrac{3\sqrt x}{\sqrt x+1}$, that are capable of raising $300\ \text{kg}$ water in $5$ minutes and $50\ \text{kg}$ water in $2$ minutes respectively from a well of $100\ \text{m}$ deep. The value of $x$ will be
Answer: (A) 16
$P_1=\dfrac{300\times10\times100}{300}=1000\ \text{W}$, $P_2=\dfrac{50\times10\times100}{120}=\dfrac{1250}{3}\ \text{W}$, so $\dfrac{P_1}{P_2}=2.4$.
$$\frac{3\sqrt x}{\sqrt x+1}=2.4\ \Rightarrow\ 0.6\sqrt x=2.4\ \Rightarrow\ x=16$$
Solution by Sreeraj P, M.Sc Physics