Question

A can complete a piece of work in 18 days. B is 20% more efficient than A. The number of days B takes to complete the same piece of work is ?

• A. 15
• B. 12
• C. 10
• D. 9

Answer 1

The correct option is A 15

Efficiency is inversely proportional to the number of days needed to do the work.

More efficiency means less number of days needed to complete the work.

If efficiency of $A$ is $100,$ then efficiency of $B$ is $20\%$ more that is $120.$

The ratios of efficiency of $A$ and $B$ is

$\Rightarrow$ $\frac{A}{B}$ (efficiency) $=\frac{100}{120}=\frac{5}{6}$

A completes the work in $18$ days and let $B$ complete the work in $x$ days.

The ratio of number of days needed to complete the work by $A$ and $B$ is,

$\Rightarrow$ $\frac{A}{B}$ (days) $=\frac{18}{x}$

Now efficiency is inversely proportional to number of days so $\frac{A}{B}$ is

$\Rightarrow$ $\frac{5}{6}$ $=\frac{x}{18}$

$\Rightarrow$ $6\times x=5\times 18$

$\Rightarrow$ $x=15$ days

$\Rightarrow$ $B$ would complete the work in $15$ days.