Question : Pipe X can fill a tank in 20 hours and pipe Y can fill the tank in 35 hours. Both the pipes are opened at alternate hours. If pipe Y was opened first, then how much time (in hours) does it take to fill the tank?
Option 1: $\frac{269}{11}$
Option 2: $\frac{286}{11}$
Option 3: $\frac{179}{7}$
Option 4: $\frac{172}{7}$
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Correct Answer: $\frac{179}{7}$
Solution :
Given: Pipe X can fill a tank in 20 hours.
Pipe Y can fill the tank in 35 hours.
Let the capacity of the tank = LCM of 20 and 35 = 140 units
Efficiency of X per hour = $\frac{140}{20}$ = 7 units
Efficiency of Y per hour = $\frac{140}{35}$ = 4 units
Pipe Y and pipe X are alternatively opened,
Tank filled in 2 hours = 7 + 4 = 11 units
So, the tank filled in 24 hours = 11 × 12 = 132 units
In the 25
th
hour, it is Y's turn and the tank will be filled = 132 + 4 = 136 units
The remaining (140 – 136) = 4 units will be filled by X in $\frac{4}{7}$ hours.
So, the total time = (25 + $\frac{4}{7}$) hours = $\frac{179}{7}$ hours
Hence, the correct answer is $\frac{179}{7}$ hours.
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