Question

Arun can finish a work in 12 days; Ajit can finish the same work in 15 days while Amit can finish the same work in 20 days. Find the total time taken when all three work together to complete the work.

• A. 6 days
• B. 5 days
• C. 4 days
• D. 3 days
• E. 6 (1/2) days

Answer 1

The correct option is B 5 days

Arun can finish $100\%$ of work in 12 days he can finish $\left(\frac{100}{12}\right)=8.33\%$ of the work in a day.

Ajit can finish $100\%$ of work in 15 days he can finish $\left(\frac{100}{15}\right)=6.67\%$ of the work in a day.

Amit can finish $100\%$ of the work in 20 days he can finish $\left(\frac{100}{20}\right)=5\%$ of the work in a day.

So, if all three work together, then they can finish $(8.33+6.67+5)\%=20\%$ of the work in a day.

So, they can complete the work in $\left(\frac{100}{20}\right)$ = 5 days. Hence option (B).

2nd method:- W= 12A=15B=20C .

$n(A+B+C)=12A,n(A+\frac{3}{4}A+\frac{3}{5}A)=12A,n=5days$. Option (2).