Rohit purchased a cistern which had a leakage. The cistern can be filled by two inlet pipes, which can individually fill the cistern in 12 min and 15 min respectively. Despite leakage, the two inlet pipes together can fill the cistern in 20 min. How long will it take to empty the completely full the cistern due to leakage?
Explanation:
Let, the total capacity of cistern be LCM (12,15,20) = 60 units
∴ Rate of the two inlet pipes are 60/12 = 5 units per minute and 60/15 = 4 units per minute.
Also, rate of filling of cistern along with the leakage = 60/20 = 3 units per minute
∴ Rate of leakage (L) = 3 – (5 + 4) = -6 units per minute. (-ve indicates that leakage is emptying the tank)
∴ Time taken by leakage to empty the cistern = 60/6 = 10 mins
Hence, option (a).
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