Question

A can fill a tank in 20 hours while B can empty the same tank in 15 hours. Both pipes are employed on a half-filled tank and after 10 hours A is replaced by a pipe whose efficiency is double that of A, the time required to fill the tank (in hours) is
1. 20
2. 25
3. 30
4. 32
5. 35

Answer 1

Correct Answer - Option 3 : 30

Given:-

Time for A to fill the tank = 20 hours

Time for B to empty the tank = 15 hours

Time taken for replaced pipe to fill the tank = 10 hours (double efficiency than A)

Concept used:-

Considering capacity of tank equal to LCM of filling and emptying pipes/ \leaks.

Calculation:-

Capacity of tank = LCM of (20, 15 and 10) = 60 units

Work done by A in 1 hour = 60 / 20 = 3 units.

Work done by B in 1 hour = -60 / 15 = - 4 units. [Negative sign indicates that pipe B empties the tank]

Work done by replaced pipe in 1 hour = 60 / 10 = 6 units.

Initially filled tank = 30 units (half filled)

For 10 hours, A and B are used.

Tank filled after 10 hours = 30 + [10 × (3 – 4)] = 20 units

Time required to fill remaining 40 units when A is replaced = 40 / (6 – 4) = 20 hours.

Total time = 10 + 20 = 30 hours.