Pipe A and B can fill a tank in 15 hours and 20 hours respectively. Pipe C can empty the tank in 25 hours. Pipes A, B and C works together but pipe C is closed after 10 hours, then time taken by pipe A and B to fill the remaining tank is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2 hours
In one hour, A fills \(\frac{1}{15}\) of the tank, B fills \(\frac{1}{20}\) and C empties \(\frac{1}{25}\). With all three open:
\( \displaystyle \frac{1}{15} + \frac{1}{20} - \frac{1}{25} = \frac{20 + 15 - 12}{300} = \frac{23}{300} \)
In 10 hours they fill
\( \displaystyle 10 \times \frac{23}{300} = \frac{23}{30} \)
so \(\frac{7}{30}\) of the tank is left. A and B together fill per hour
\( \displaystyle \frac{1}{15} + \frac{1}{20} = \frac{7}{60} \)
\( \displaystyle \text{Time} = \frac{7}{30} \div \frac{7}{60} = 2 \text{ hours} \)