Question

Rajesh, Mahesh and Suresh divide a work amongst themselves in the ratio 2 : 3 : 5. Their rates of doing the work are in the ratio 1 : 2: 3. It takes Rajesh 12 days to complete his part . What is the amount of work completed by them in 8 days from the start ?

• A.
• B.
• C.
• D.
• E.

Answer 1

The correct option is A

Proportion of work done by Rajesh , Mahesh and Suresh is $\frac{2}{10},\frac{3}{10}$ and $\frac{5}{10}$ respectively.
Rate of doing work are in the ratio – 1:2:3
$\therefore$ The time required to complete the work are in the ratio - $1$ : $\frac{1}{2}:\frac{1}{3}$
Let, Rajesh complete the entire work in ‘x’ days.
$\therefore$ Work done by Rajesh in 1 day = $\frac{1}{x}$
According to Question,
$\left(\frac{1}{x}\right)\times 12=\frac{2}{10}$
$\Rightarrow$ x = 60 days.
Thus, Mahesh and Suresh will complete the work in 30 and 20 days respectively.
$\therefore$ Total work done by three of them in 8 days = $(\frac{1}{60}+\frac{2}{60}+\frac{3}{60})\times 8=\frac{4}{5}$