Question

A cistern can be filled by one tap in $5$ hours and by another in $4$ hours. How long will it take to fill if both the taps are opened simultaneously?

• A. $\frac{10}{9}hrs$
• B. $9hrs$
• C. $10hrs$
• D. $\frac{20}{9}hrs$

Answer 1

Answer: (D)

$\frac{20}{9}hrs$

Time taken by first tap to fill the cistern $=5$ hours.
Work done by first tap in $1$ hour $=\frac{1}{5}$
Time taken by second tap to fill the cistern $=4hours$.
Work done by second tap in $1$ hour $=\frac{1}{4}$
Work done by (first tap + second tap) in $1$ hour $=\frac{1}{5}+\frac{1}{4}=\frac{9}{20}$
Therefore, time taken by (first tap + second tap) to fill the cistern $=\frac{20}{9}hours$.