Question

Three taps A, B and C can fill a tank in 12, 15 and 20 h respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be filled in

• A. 6h
• B. 7h
• C. 5h
• D. None of these

Answer 1

Answer: (B)

7h

Answer 2

Filling done by pipe A and B in 1 hour $=\frac{1}{12}+\frac{1}{15}=\frac{3}{20}$

Filling done by pipe A and C in 1 I hour $=\frac{1}{12}+\frac{1}{20}=\frac{2}{15}$

Filling done in first 2 hour $=\frac{3}{20}+\frac{2}{15}=\frac{17}{60}$

Filling done in 6 hour $=\frac{17}{60}\times3=\frac{51}{60}$

Remaining filling $=1-\frac{51}{60}=\frac{3}{20}$

Now in 7th hour, filling done by A and B, $=\frac{\frac{3}{20}}{\frac{3}{20}}=1$ h
So total time $=7$ hours
The correct option is (B)