Question

A can do one third of a work in 6 days. b can do two fifth of a work in 12 days

Answer 1

Complete Question:

A can do one-third of work in 6 days. b can do two-fifth of work in 12 days. In how many days both A and B together can do the work?

Given:

A can do one-third of work in 6 days

B can do two-fifth of work in 12 days

To find:

In how many days both A and B together can do the work?

Solution:

If in 6 days, A can do = $\frac{1}{3} rd$ of a work

Then, in 1 day, A can do = $\frac{1}{6\times 3} = \frac{1}{18}$ of a work

and

If in 12 days, B can do = $\frac{2}{5} th$ of a work

Then, in 1 day, B can do = $\frac{2}{5\times 12} = \frac{2}{60} = \frac{1}{30}$ of a work

Now,

In 1 day, A & B together will finish,

= $\frac{1}{18} + \frac{1}{30}$

= $\frac{5 + 3}{90}$

= $\frac{8}{90}$

= $\bold{\frac{4}{45}}$ of the work

Thus, both A and B together can do the work in $\underline{\frac{45}{4} \:days}$ or $\underline{11\frac{1}{4} \:days}$.

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