B is 20% more efficient than a. B started the work & did it for x days. And then b is replaced by a. A completed the remaining work in x+8 days. Ratio of work done by a & b is 2:3. In how many days a & b working together can complete the whole work?
Answers
Given : B is 20% more efficient than A
B started the work & did it for x days.
And then b is replaced by a. A completed the remaining work in x+8 days.
Ratio of work done by A & B is 2:3.
To Find : In how many days A & B working together can complete the whole work
Solution:
A' s 1 day work = k
B is 20% more efficient than A
=> B's 1 day work = k + (20/100)k = 1.2k
Work done by B in x days = 1.2kx
Work done by A in x+8 days = k ( x + 8)
Ratio of work done by A & B is 2 : 3
=> k ( x + 8) / 1.2kx = 2 /3
=> 3x + 24 = 2.4x
=> 0.6x = 24
=> x = - 40
Hence mistake in data
Assuming Ratio of work done by A & B is 3 : 2
=> k ( x + 8) / 1.2kx = 3/2
=> 2x + 16 = 3.6x
=> 1.6x = 16
=> x = 10
Work done by B in x days = 1.2*k *10 = 12k
Work done by A in x+8 days = k ( 10 + 8) = 18k
Total Work = 12k + 18k = 30k
Total work in 1 day = k + 1.2k = 2.2k
Time taken = 30k/2.2k = 13.63
A & B working together can complete the whole work in 13.63 days
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