Correct Answer - Option 4 : 127 hours

**Given:**

Pipe M can fill the cistern in = 8 hours

Pipe N can empty the cistern in = 9 hours

**Calculation:**

Let the total capacity of cistern be LCM (8, 9) = 72 litres

Now,

Cistern filled by M in 1 hour = 72/8

⇒ 9 litre/hour

Cistern empty by N in 1 hour = 72/9

⇒ (– 8) litre/hour

Cistern filled by (M + N) in 1 hour = (9 – 8)

⇒ 1 litre/hour

Now,

According to the question,

For first hour Pipe M is opened = 9 litre

For second hour Pipe N is opened = (– 8) litre

For third hour Pipe M is opened = 9 litre

For fourth hour Pipe N is opened = (– 8) litre

Similarly, So…. On

Now,

We conclude that –

2 hours = 1 litre

× 63 × 63

126 hours = 63 litre

__+1 hours = +9 litre__

127 hours = 72 litres

**∴**** The Cistern will be filled in 127 hours.**