Pipe R can empty a full tank in 30 hours. But two pipes P and Q can fill the tank in 15 hours and 10 hours, re

Question

Pipe R can empty a full tank in 30 hours. But two pipes P and Q can fill the tank in 15 hours and 10 hours, respectively. Ram unknowingly opened all three taps. After 2 hours Shyam realised it and closed Pipe R. Due to this mistake how much time more would it take to fill the tank?

Examoogle · Accepted Answer

The correct answer is Option B: 24 min. Calculate individual efficiencies: P=2, Q=3, R=-1. Net efficiency for first 2 hours = (2+3-1)=4 units/hr. 2 hours work = 8 units. Remaining = 22 units. New efficiency (P+Q) = 2+3=5. Time = 22/5 = 4.4 hours. Total time is 4.4, but the question asks 'how much time more', which usually implies total time needed minus the 2 hours already passed = 4.4 - 2 = 2.4 hours (2 hours 24 minutes).

Step-by-Step Solution & Concepts:
Shortcut Trick: Calculate individual efficiencies: P=2, Q=3, R=-1. Net efficiency for first 2 hours = (2+3-1)=4 units/hr. 2 hours work = 8 units. Remaining = 22 units. New efficiency (P+Q) = 2+3=5. Time = 22/5 = 4.4 hours. Total time is 4.4, but the question asks 'how much time more', which usually implies total time needed minus the 2 hours already passed = 4.4 - 2 = 2.4 hours (2 hours 24 minutes).

Formula Used: $$Total Capacity = LCM(15, 10, 30) = 30 	ext{ units}$$, $$Efficiency = \frac{Work}{Time}$$, $$Time = \frac{Remaining Work}{Efficiency}$$

Given: Pipe R empties in 30 hours, Pipe P fills in 15 hours, Pipe Q fills in 10 hours. All three pipes are open for 2 hours, then R is closed.

Steps: Calculate Efficiencies: Assuming total tank capacity is the LCM of (15, 10, 30) = 30 units. The efficiencies are: P = 30/15 = +2, Q = 30/10 = +3, R = 30/30 = -1 (since it empties).. Work Done in First 2 Hours: With all three pipes open, net efficiency is $2 + 3 - 1 = 4$ units/hr. In 2 hours, they fill $4 	imes 2 = 8$ units.. Calculate Remaining Work: After 2 hours, remaining capacity = Total Capacity - Work Done = $30 - 8 = 22$ units.. Calculate Additional Time: After closing R, only P and Q work. New efficiency = $2 + 3 = 5$ units/hr. Time required = $22 / 5 = 4.4$ hours. $0.4 	ext{ hours} = 0.4 	imes 60 = 24$ minutes.

Answer: B is correct because the remaining 22 units filled by pipes P and Q at 5 units/hour take 4.4 hours, which is 4 hours 24 minutes.

Exam Tip: This is a standard Time and Work variation; always treat inlet pipes as positive and outlet pipes as negative efficiency.

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