Question

A cistern can be filled by pipes M and N in 5 hours and 10 hours respectively. While another pipe Q empty the cistern in 20 hr. If all three pipes opened simultaneously then, in how many hours can the cistern be filled?

1. 4 hours
2. 2 hours
3. 5 hours
4. 3 hours
5. None of these

Answer 1

Correct Answer - Option 1 : 4 hours

Given:

Pipe M can fill in = 5 hr

Pipe N can fill in = 10 hr

Pipe Q can empty in = 20 hr

Calculation:

Let the total capacity of cistern be LCM (5, 10, 20) = 20 litres

Now,

Cistern filled by M in 1 hour = 20/5

⇒ 4 litre/hour

Cistern filled by N in 1 hour = 20/10

⇒ 2 litre/hour

Cistern empty by Q in 1 hour = 20/20

⇒ 1 litre/hour

Now,

Required time = Total capacity of cistern/Total efficiency

⇒ 20/(4 + 2 – 1)

⇒ 20/5

⇒ 4

∴ The cistern can be filled in 4 hours