There are two drains, A and B in the bottom of a water tank. If only A is open, it takes 30 minutes to empty the full tank and if only B is open, it takes 20 minutes. If both drains are open for 10 minutes, then B is closed, how much time does take to empty a full tank?

Explanation

Part of tank, empty by drain A in 1 min = $\frac{1}{30}$ Part of tank, empty by drain B in 1 min = $\frac{1}{20}$ Part of tank, empty by both drains in 1 min = $(\frac{1}{30} + \frac{1}{20})$ Part Part of tank, empty by both drains A and B in 10 min. = $(\frac{1}{30} + \frac{1}{20})$ Part = $\frac{1}{3} + \frac{1}{2} \Rightarrow \frac{5}{6}$ Part Remaining, $1 - \frac{5}{6} \Rightarrow \frac{1}{6}$ Part Time taken by drain A, to empty part of tank = 30 minutes Time taken by drain A to empty remaining part of tank = $\frac{1}{6} \times 30 \Rightarrow 5$ min. Total time taken to empty full tank = $(10 + 5)$ min. = 15 min. So, option (b) is correct answer. ## Page 14 ## Simple Interest and Compound Interest