Two pipes can separately fill a tank in 20 hours and 30 hours respectively. Both the pipes are opened to fill the tank but when the tank is 3/4th full, a leak develops in, through which one-fourth of water supplied by both the pipes goes out. What is the total time taken to fill the tank?
Explanation:
Time to completely fill the tank by the two pipe:
1/20 + 1/30= 1/n
⇒ n = 12 hours
So, 3/4th of the tank will be filled in 3/4 × 12 = 9 hours.
Remaining time = 12 – 9 = 3 hours.
But, for the remaining 1/4th of the tank, the combined efficiency drops to 3/4th (1/4th is getting leaked),
∴ Time required will be come 4/3 times, i.e. 4/3 × 3 = 4 hours.
Hence, total time taken to fill the tank = 9 + 4 = 13 hours.
Hence, option (d).
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