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.