Question

A tank 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 tank from empty state if b is used for the first half time and then a and b fill it together for the other half.

Answer 1

Let the part of tank filled(in 1 minute) by,
A = 1/60
B-= 1/40
Let the time taken = x
So, x/2(1/60) + x/2(1/40) = 1
x/120 + x/80 = 1
x= 48

Answer 2

Let the total time be x mins.
Part filled in first half means in x/2 = 1/40

Part filled in second half means in x/2 = \begin{aligned}
\frac{1}{60}+\frac{1}{40} \\
= \frac{1}{24} \\
\text{ Total = } \\
\frac{x}{2}*\frac{1}{40} + \frac{x}{2}*\frac{1}{24} = 1 \\

=> \frac{x}{2} \left(\frac{1}{40}+\frac{1}{24} \right) = 1 \\
=> \frac{x}{2}*\frac{1}{15} = 1 \\
=> x = 30 mins
\end{aligned}
Source :- Google