Question

A can do a piece of work in 40 days , He worked at it for 5 days then B finished it in 21 days. The number of days that A and B take together to finish the work are

• A. 15 days
• B. 14 days
• C. 13 days
• D. 10 days

Answer 1

The correct option is A 15 days

A completed one work in 40 days that means he do $\frac{1}{40}$ unit work per day

Now Let B completed the same work in x days

According to question we have

$\frac{5}{40}+\frac{21}{x}=1$

$\frac{21}{x}=\frac{35}{40}$

$x=24$

Now let A and B together finish the same work in y days

So we have

$y(\frac{1}{40}+\frac{1}{24})=1$

On solving, we have

$y=15$