Question

A and B can do a work individually in 21 and 35 days respectively. In how many days can they complete the work, working alternatively?

Answer 1

let total work is 105 unit
A can do 105/21 = 5 units/day.
B can do 3 units /day.
Suppose A starts the work.
So 1st day A will do 5 units.
2nd day B will do 3 units.
5+3+5+3+5+3+......( they will do the work alternatively)
105=(13*8)+1
means to complete 105 units work (13*2) days + (1/5) will need...
= 26.2 days will need to complete the work..

Answer 2

Given:

A can do a work in 21 days.

B can do a work in 35 days.

To find:

In how many days can they complete the work if they work alternatively.

Solution:

To find the total work done,

Find the LCM of the numbers 21 and 35,

Hence, the total work done = 105.

For A,

The work done = 21 / 105

A = 1 / 5 in a day.

For B,

The work done = 35 / 105

B = 1 / 3 in a day.

B can do 3 units /day.

Suppose A starts the work.

Day 1 = A

Day 2 = B

Day 3 = A

And so on,

1/5 + 1/3 + 1/5 + 1/3 ... = 105

Therefore,

It takes 26.2 days to complete the work if they work alternatively.

Hence, 26.2 days is the answer.