Two pipes can fill a cistern separately in 36 minutes and 45 minutes, respectively. A waste pipe can drain off 40 litres per minute. If all the three pipes are opened, the cistern fills in one hour. The capacity (in litres of the cistern) is:
- AOption (a)
600
- BOption (b)
1200
- COption (c)
300
- DOption (d)
400
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Correct answer
1200
Why this answer is correct
Given:
Two pipes can fill a cistern separately in 36 minutes and 45 minutes, respectively.
A waste pipe can drain off 40 litres per minute.
If all three pipes are opened, the cistern fills in one hour.
Formula used:
Let the capacity of the cistern be x litres.
Rate of filling by the first pipe = x / 36 litres/minute
Rate of filling by the second pipe = x / 45 litres/minute
Rate of emptying by the waste pipe = 40 litres/minute
Net rate of filling when all three pipes are open = (x / 36) + (x / 45) - 40 litres/minute
Calculation:
The cistern fills in 60 minutes (1 hour), so:
⇒ (x / 36) + (x / 45) - 40 = x / 60
⇒ (5x / 180) + (4x / 180) - 40 = x / 60
⇒ (9x / 180) - 40 = x / 60
⇒ (1 / 20)x - 40 = x / 60
⇒ 3x - 2400 = x
⇒ 3x - x = 2400
⇒ 2x = 2400
⇒ x = 1200
∴ The capacity of the cistern is 1200 litres.




















