Pipe A, pipe B and pipe C together can fill a tank in 20 minutes, but because of the leak all three pipes take

Question

Pipe A, pipe B and pipe C together can fill a tank in 20 minutes, but because of the leak all three pipes take 10 minutes more time to fill the tank completely. Find the time in which leak can empty the full tank.

Examoogle · Accepted Answer

The correct answer is Option B: 60 min. Use the formula $T_{leak} = \frac{T_1 	imes T_2}{T_2 - T_1}$ where $T_1 = 20$ and $T_2 = 30$. Calculation: $(20 	imes 30) / (30 - 20) = 600 / 10 = 60$.

Step-by-Step Solution & Concepts:
Shortcut Trick: Use the formula $T_{leak} = \frac{T_1 	imes T_2}{T_2 - T_1}$ where $T_1 = 20$ and $T_2 = 30$. Calculation: $(20 	imes 30) / (30 - 20) = 600 / 10 = 60$.

Formula Used: $$\frac{1}{T_{net}} = \frac{1}{T_{fill}} - \frac{1}{T_{leak}}$$

Given: Combined rate of Pipe A, B, and C = 1/20 tank/min. Time taken with leak = 20 + 10 = 30 minutes.

Steps: Define rates: Let $R_{fill}$ be the filling rate of pipes (A+B+C) and $R_{leak}$ be the emptying rate of the leak. The filling rate is $1/20$ tank/min.. Calculate effective rate: With the leak, the total time is $20 + 10 = 30$ minutes. The effective filling rate is $1/30$ tank/min.. Find leak rate: Using the relation $R_{eff} = R_{fill} - R_{leak}$, we get $R_{leak} = R_{fill} - R_{eff} = 1/20 - 1/30$.. Final answer: The time required for the leak to empty the full tank is the reciprocal of the leak rate.

Answer: B is correct because the leak reduces the effective net rate to 1/30 tank per minute, resulting in a time of 60 minutes to empty the tank.

Exam Tip: This concept of 'Net Rate = Gross Rate - Loss Rate' is identical to relative speed problems where $V_{net} = V_1 - V_2$ for objects moving in opposite directions.

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