Question

A set of 10 pipes (set x) can fill 70% of a tank in 7 minutes. Another set of 5 pipes (set y) flls 3/8 of the tank in 3 minutes. A third set of 8 pipes (set z) can empty 5/10 of the tank in 10 minutes. How many minutes will it take to fill the tank if all the 23 pipes are opened at the same time?

Answer 1

The time required to fill the tank completely = $\frac{40}{7}$ minutes

Step-by-step explanation:

It is given that pipes of set x can fill 70% of the tank in 7 min.

• set x =$\frac{70}{100}th$ in 7 min  

It means that, $\frac{1}{10}th$ tank is filled in 1 min.

Similarly,  

It is given that pipes of set y can fill $\frac{3}{8}th$ of the tank in 3 min.

So, we write as,

• set y = $\frac{3}{8}th$ of tank in 3 min  

It means that, $\frac{1}{8}th$ tank is filled in 1 min.

And,  pipes of the set z can empty $\frac{5}{10}$th  of the tank in 10 min.

• set z = $\frac{5}{10}th$  in 10 min  

Therefore, $\frac{1}{20} th$  tank is emptied in 1 min.

So,  we consider all three sets for one minute. Then,

$\frac{1}{10} + \frac{1}{8} -\frac{1}{20} = \frac{7}{40}$th tank is filled in one minute.

Thus, the time required to fill the tank completely =$\frac{40}{7}$ minutes