Question

Kim can do a work in $3$ days while David can do the same work in $2$ days. Both of them finish the work together and get $Rs.150.$ What is the share of Kim ?

• A. $Rs.30$
• B. $Rs.60$
• C. $Rs.70$
• D. $Rs.75$

Answer 1

The correct option is A $Rs.30$

Kim can do a work in $3$ days $\Rightarrow$ In $1$ day Kim does $\frac{1}{3}$ units of work

David can do the same work in $2$ days $\Rightarrow$ In $1$ day David does $\frac{1}{2}$ units of work

$\therefore$ Together they do $=(\frac{1}{3}+\frac{1}{2})=\frac{5}{6}$ units of work in a day

$\therefore$ Together they can complete the work in $\frac{6}{5}=1.2$ days

Ratio of work of Kim to David in a day $=\frac{1/3}{1/2}=\frac{2}{3}=2:3$

$\therefore$ the total share will be divided in the same ratio as their share of work $=$ Kim $:$ David $=2:3$

$\therefore$ $2x+3x=150$

$\Rightarrow 5x=150$

$\Rightarrow x=30$

$\therefore$ Kim's share is $30\times 2=60$

and David's share is $30\times 3=90$

$\therefore$ Answer : Option B.