Question : A1 alone can do a work in 12 days and A2 alone can do the same work in 15 days. With help of A3, they finish the same work in 5 days. In how many days A3 alone can do the same work?
Option 1: 16
Option 2: 20
Option 3: 24
Option 4: 27
Correct Answer: 20
Solution :
Time taken by A1 to do the work = 12 days
Part of work done by A1 in a day = $\frac{1}{12}$
Time taken by A2 to do the work = 15 days
Part of work done by A2 in a day = $\frac{1}{15}$
Let $x$ be the time taken by A3 to do the work.
Part of work done by A3 in a day = $\frac{1}{x}$
Time taken by A1, A2 and A3 to do the work = 5 days
Part of work done by A1, A2 and A3 in a day = $\frac{1}{5}$
$\frac{1}{12}$ + $\frac{1}{15}$ + $\frac{1}{x}$ = $\frac{1}{5}$
⇒ $\frac{1}{x}$ = $\frac{1}{5}$ – ($\frac{1}{12}$ + $\frac{1}{15}$)
⇒ $\frac{1}{x}$ = $\frac{12-5-4}{60}$
⇒ $\frac{1}{x}$ = $\frac{3}{60}$
⇒ $\frac{1}{x}$ = $\frac{1}{20}$
⇒ $x$ = 20 days
Hence, the correct answer is 20.
Related Questions
Know More about
Staff Selection Commission Multi Tasking ...
Application | Cutoff | Selection Process | Preparation Tips | Eligibility | Exam Pattern | Admit Card
Get Updates Brochure
Your Staff Selection Commission Multi Tasking Staff Exam brochure has been successfully mailed to your registered email id “”.
