One fifth of a tank is filled by pipe at the rate of 10 lit/h, three - fifth of a tank is filled by pipe at the rate of 15 lit/h and rest at the rate of 5 lit/h. If average rate of pipe at which tank will completely get filled is 'A' lit/hr then, find the value of 'A'?

Option 2 : 10

Let the total capacity of a tank be ‘m’ litres

Average rate = total distance/time taken

⇒ Time taken by a pipe to fill 1/5^th of a tank = (m/5)/10 = m/50 hr

⇒ Time taken by a pipe to fill 3/5^th of a tank = (3m/5)/15 = m/25 hr

⇒ Rest part of a tank remain to fill = m {1 – (1/5 + 3/5)} = m (1 – 4/5)

⇒ Rest part of a tank remain to fill = m/5

⇒ Time taken by a pipe to fill rest of tank = (m/5)/5 = m/25 hr

Total time taken by a pipe to fill tank completely =

= (m/50 + m/25 + m/25)

= 5m/50

= m/10

Average rate to fill tank completely =

⇒ A = Total capacity of a tank/Total time taken by a pipe to fill tank completely

⇒ A = m/ (m/10)                                

⇒ 10 lit/hr

∴ Average rate at which tank will completely get filled is 10 lit/hr.

Alternate Solution: Let the total tank capacity be 50 litres

Then total time = 1 + 2 + 2 = 5 hours