Question

A can do $\frac{1}{5}$th of a work in 4 days and B can do $\frac{1}{6}$th of the same work in 5 days. In how many days they can finish the work, if they work together?

• A. 12
• B. 20
• C. 15
• D. 30

Answer 1

Answer:

A. 12

Solution;

A can do $\frac{1}{5}$th work in 4days.

Efficiency of A = $\frac{1}{4\times5}=\frac{1}{20}$

B can do $\frac{1}{6}$th of the work in 5days.

Efficiency of B = $\frac{1}{6\times5}=\frac{1}{30}$

Combined Efficiency of A and B is = $\frac{1}{20}+\frac{1}{30}$

$=\frac{3+2}{60}=\frac{5}{60}=\frac{1}{12}$

A and B together can complete the work in 12 days.

Shortcut:

A can do 1/5^th of a work in = 4 days

A can do the whole work in = $4\times 5 = 20 days$

B can do 1/6^th of the same work in = 5 days

B can do the whole work in = $5 \times 6 = 30 days$

From the following figure

Total work = 60

Total efficiency of A and B = 2 + 3 = 5

A and B together can complete the whole work in = $\frac{60}{5} = 12 days$