Question

Two ducts X and Y and can fill a cistern in 24 minutes and 30 minutes respectively but a third duct Z can empty the full tank in 12 minutes. X and Y are kept open for 10 minutes in the beginning and then Z is also opened. In what time is the cistern emptied?

• A. 90 mins
• B. 100 mins
• C. 60 mins
• D. 50 mins
• E. 110 mins

Answer 1

The correct option is A

90 mins

For 10 minutes $=10(\frac{1}{24}+\frac{1}{30})=\frac{3}{4}$

When all the three pipes are opened $=\frac{1}{24}+\frac{1}{30}-\frac{1}{12}=-1/120$

Empty the cistern in 1 min is $\frac{1}{120}$

Therefore, $\frac{3}{4}$ will empty in $\frac{3}{4}$$\times$ 120 = 90 minutes.