1.

Two pipes A and B can fill a tank in 8 h and 12 h respectively. A waste pipe C can empty the tank in 4 h. A and B are kept open for 2 h, then C is also opened. Then the tank will empty in1. 5 h2. 6 h3. 7 h4. 10 h

Answer» Correct Answer - Option 4 : 10 h

Given:

Time taken by A to fill the tank = 8 h

Time taken by B to fill the same tank = 12 h

Time taken by C to empty the tank = 4 h

Concept used:

If a tap can fill a tank in X h, part of the tank filled in 1 h = 1 / X

For outlet pipe, efficiency should be taken with negative sign

Part filled by A in 1 h = 1 / 8

Part filled by B in 1 h = 1 / 12

Part empty by C in 1 h = 1 / 4

Part filled by (A + B) in 2 h = (1 / 8 + 1 / 12) × 2 = 5 / 24 × 2 = 5 / 12

Now, C is also opened

∴ Part fill / empty in 1 h = 1 / 8 + 1 / 12 + (-1 / 4) = -1 / 24

Here, negative sign shows the tank get empty when (A + B + C) opened together

∵ 1 / 24 part empty in 1 h

∴ 5 / 12 part will get empty in = 24 × 5 / 12 = 10 h

Therefore, tank will get empty in 10 h


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