Question

a can do a piece of work in 4 days and B can complete the same work in 12 days in how many days will they be able to complete the work if they work together​

Answer 1

Question:

A can do a piece of work in 4 days and B can complete the same work in 12 days, in how many days will they be able to complete the work if they work together​?

Answer:

If they work together then they will complete the work in 3 days.

Given:

A can do the piece of work in 4 days.

B can do the piece of work in 12 days.

To find:

If A and B work together then in how many days they will complete the work.

Explanation:

A can do the piece of work in 4 days.

∴ In 1 day A can do = $\frac{1}{4}$ part of the work.

B can do the work in 12 days.

∴ In 1 day B can do = $\frac{1}{12}$ part of the work.

∴ In 1 day A and B together can do_

$(\frac{1}{4} + \frac{1}{12})$

= $(\frac{3+1}{12} )$ [ ∵ The L.C.M. of the denominators is 12.]

= $\frac{4}{12}$

= $\frac{1}{3}$ parts of the work.

Hence,

$\frac{1}{3}$ part of the work A and B can do in 1 day.

∴ 1 part of the work A an B can do in ( 1 × 3) days

                                                        = 3 days.

∴ To complete the work together A and B will take 3 days.

Answer 2

If they work together then they will complete the work in 3 days.

Given:

A can do the piece of work in 4 days.

B can do the piece of work in 12 days.

To find

If A and B work together then in how many days they will complete the work.

Explanation:

A can do the piece of work in 4 days.

∴ In 1 day A can do = 1/4part of the work.

B can do the work in 12 days.

∴ In 1 day B can do = 1/12 part of the work.

∴ In 1 day A and B together can do = 1/4+1/12

∵ The L.C.M. of the denominators is 12.

3+1/12

=4/12

=1/3 part of the work A and B can do in 1 day.

∴ 1 part of the work A an B can do in ( 1 × 3) days

= 3 days.

∴ To complete the work together A and B will take 3 days.