There are two pipes used to fill a tank and when operated together, they can fill the tank in 20 minutes. If one pipe can fill the tank two and a half times as quickly as the other, then the faster pipe alone can fill the tank in:

Correct option is D

Given:

Two pipes fill a tank together in 20 minutes.

One pipe fills the tank 2.5 times as quickly as the other.

Solution:

the slower pipe's rate be ( x ) tanks per minute.

Then, the faster pipe's rate is ( 2.5x ) tanks per minute.

x + 2.5x = 3.5x tanks per minute

​$$\frac{1}{3.5x}$$​ = 20minutes

3.5x = $$\frac{1}{20} \implies x = \frac{1}{20 \times 3.5} = \frac{1}{70}$$​ tanks per minute

2.5x = $$2.5 \times \frac{1}{70} = \frac{2.5}{70} = \frac{1}{28}$$​ tanks per minute

​$$\frac{1}{\frac{1}{28}}$$ = 28  minutes  -