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 take all the four inlets to fill up the dam?

• A. $8min$
• B. $10min$
• C. $12min$
• D. None of these

Answer 1

Answer: (B)

$10min$

Let Pipes be A,B ,C and D
$\frac{1}{A}+\frac{1}{B}+\frac{1}{C}=\frac{1}{12}$
$\frac{1}{B}+\frac{1}{C}+\frac{1}{D}=\frac{1}{15}$
$\frac{1}{A}+\frac{1}{D}=\frac{1}{20}$
Adding all equations
$2[\frac{1}{A}+\frac{1}{B}+\frac{1}{C}+\frac{1}{D}]=\frac{1}{12}+\frac{1}{15}+\frac{1}{20}=\frac{1}{5}$
$\frac{1}{A}+\frac{1}{B}+\frac{1}{C}+\frac{1}{D}=\frac{1}{10}min$
All the inlets together can fill in 10 min