A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?

15 min

20 min

27.5 min

30 min

Explanation:

Part filled by $\left(A + B\right)$ in 1 minute =$ \left(\dfrac{1}{60} +\dfrac{1}{40} \right) $=$ \dfrac{1}{24} $.

Suppose the tank is filled in $ x $ minutes.

Then,$ \dfrac{x}{2} \left(\dfrac{1}{24} +\dfrac{1}{40} \right) $= 1

$\Rightarrow \dfrac{x}{2} $x$ \dfrac{1}{15} $= 1

$\Rightarrow x $ = 30 min.