Question

Choose the correct answer from the alternatives given.
Two pipes A and B can fill a cistern in 20 minutes and 25 minutes respectively. Both the pipes are opened together, but at the end of 5 minutes the first is turned off. How long does it take to fill the cistern?

• A. 10 min
• B. $13\frac{3}{4}$ min
• C. 17 min
• D. 20 min

Answer 1

The correct option is B $13\frac{3}{4}$ min

Let the total capacity be 100 units. [LCM of 20 & 25]
Pipes A fills = $\frac{100}{20}$= 5 units/minute.
Pipes B fills = $\frac{100}{25}$ = 4 units / minute.
Let the time taken by pipe B be x minutes.
According to the question,
(5+4) $\times 5+4\times x=100$
9 $\times$ 5 + 4x = 100
4x = 55
x= $\frac{55}{4}=13\frac{3}{4}min$.