Question

A and B can do a piece of work in 21 and 24 days respectively. They start the work together and after some days A leaves the work and B completes the remaining work in 9 days. After how many days did A leave?

• A. 5
• B. 7
• C. 8
• D. 6

Answer 1

The Correct Option is B

To find out after how many days A left the work, we first need to determine the work rate for A and B:

• A's work rate: A can complete the work in 21 days, so A's work rate is 1/21 of the work per day.
• B's work rate: B can complete the work in 24 days, so B's work rate is 1/24 of the work per day.

Let x be the number of days A worked before leaving. During these x days, both A and B work together:

The work done by A in x days = x/21.

The work done by B in x days = x/24.

Total work done by both A and B in x days = x/21 + x/24.

After A leaves, B completes the remaining work in 9 days. So, the work B does in these 9 days = 9/24 = 3/8.

The total work that needs to be done is 1 (since it is one complete piece of work). Therefore, we have:

x/21 + x/24 + 3/8 = 1

Now, solve for x:

First find the common denominator for the terms 21 and 24: the LCM is 168. The equation becomes:

(8x + 7x)/168 + 3/8 = 1

15x/168 + 3/8 = 1

Subtract 3/8 from both sides:

15x/168 = 1 - 3/8

15x/168 = 5/8

Now, solve for x:

15x = 168 * (5/8)

15x = 105

x = 105/15

x = 7

Therefore, A left the work after 7 days.