Question

The Bubna dam has four inlets. Through the first three inlets, the dam can be filled in 12 minutes; through the second, the third and the fourth inlet, it can be filled in 15 minutes; and through the first and the first inlet, in 20 minutes. How much time will it take all the four inlets to fill up the dam?

विकल्प

• 8 min

• 10 min

• 12 min

• None of these

Answer 1

10 min

Explanation:

Let Pipes be A, B, C and D

${\displaystyle \frac{1}{\text{A}}+\frac{1}{\text{B}}+\frac{1}{\text{C}}=\frac{1}{12}}$

${\displaystyle \frac{1}{\text{B}}+\frac{1}{\text{C}}+\frac{1}{\text{D}}=\frac{1}{15}}$

${\displaystyle \frac{1}{\text{A}}+\frac{1}{\text{D}}=\frac{1}{20}}$

Adding all equations

${\displaystyle 2[\frac{1}{\text{A}}+\frac{1}{\text{B}}+\frac{1}{\text{C}}+\frac{1}{\text{D}}]=\frac{1}{12}+\frac{1}{15}+\frac{1}{20}=\frac{1}{5}}$

${\displaystyle \frac{1}{\text{A}}+\frac{1}{\text{B}}+\frac{1}{\text{C}}+\frac{1}{\text{D}}=\frac{1}{10}}$ min

All the inlets together can fill in 10 min