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A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe ,then the time required by the first pipe to fill the tank alone is :

Solution

✅ Correct Option: 1

Let the second pipe take tt hours; then the first takes t+5t+5 and the third takes t−4t-4.

The condition gives 1t+5+1t=1t−4\frac{1}{t+5}+\frac{1}{t}=\frac{1}{t-4}, which simplifies to t2−8t−20=0t^2-8t-20=0, so t=10t=10.

The first pipe therefore needs 1515 hours.

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