Question

Rahul takes twice as much time as Manick and thrice as much time as Sachin to complete a job. If working together,they can complete the job in $4days$,find the time taken by each of Rahul ,Manick and Sachin separately to complete the work ?

• A. $24hr,12hr,8hr$
• B. $20hr,8hr,12hr$
• C. $16hr,4hr,8hr$
• D. $12hr,8hr,20hr$

Answer 1

The correct option is A $24hr,12hr,8hr$

Let,

Rahul takes to complete the job in $x$ hr

Manick takes to complete the job in $\frac{x}{2}$ hr

Sachin takes to complete the job in $\frac{x}{3}$ hr

$\therefore$ Amount of the job Rahul can complete in $1$ hr $=\frac{1}{x}$

Amount of the job Manick can complete in $1$ hr $=\frac{1}{\frac{x}{2}}=\frac{2}{x}$

Amount of the job Sachin can complete in $1$ hr $=\frac{1}{\frac{x}{3}}=\frac{3}{x}$

$\therefore$ The amount of the job they can complete in $4$ days,

$\frac{1}{x}+\frac{2}{x}+\frac{3}{x}=\frac{1}{4}\Rightarrow \frac{6}{x}=\frac{1}{4}\Rightarrow x=24$

Hence, Rahul can complete the job in $24$ hrs,

Manick can complete the job in $=\frac{24}{2}=12$ hrs,

and Sachin can complete the job in $=\frac{24}{3}=8$ hrs.