Question

A and B working together completes
a work in 24 days while B and C
complete the same work in 30
days If C is 20% more efficient
than B, then in how many days
working alone A will complete
the whole work?​

Answer 1

Answer:

A can do the work in 'a' days. Hence the rate of work done by A is 1/a. B can do the same work in 'b' days. Hence rate of work done by B is 1/b. C can do the same work in 'c' days. Hence the rate of the work done by C is 1/c. For A and B together, rate of work done is 1/24. For B and C together, rate of work done is 1/30.

Now, rate of work done of C is 20% more than that of B. Hence 1/c / 1/b = 120%/100% = 6/5 Therefore, 1/c = (6/5)(1/b).

Now, 1/b + 1/c = 1/30

1/b + (6/5)(1/b) = 1/30

solving, (11/5)(1/b) = 1/30

1/b = 1/66

Now, 1/a + 1/b = 1/24

Therefore, 1/a + 1/66 = 1/24

1/a = 1/24 - 1/66

1/a = 7/264

Therefore, a = 264/7 days.

= 37 and 5/7 days.