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A and B can do a piece of work in 9 days and 15 days, respectively. If they work together, then the work will be completed in:
Question

A and B can do a piece of work in 9 days and 15 days, respectively. If they work together, then the work will be completed in:

A.

3 38\frac 38 ​days

B.

2 18\frac 18​days

C.

558\frac 58​ days

D.

4 58\frac 58​days

Correct option is C

Given:
A complete the work in 9 days
B complete the work in 15 days
Solution:
A’s one day work = 19\frac{1}{9}​ unit
B’s one day work = 115\frac{1}{15} ​unit
A+B’s one day work = 19+115=5+345=845\frac{1}{9} + \frac{1}{15} = \frac{5+3}{45}=\frac{8}{45}​​
A+B complete the total work in 458=558days\frac{45}{8} = 5\frac{5}{8} days 

Alternate Solution:

Efficiency of A = 3 unit
Efficiency of B = 5 unit
Time required to complete whole work by A+B together = 458=558days\frac{45}{8} = 5\frac{5}{8} days​​

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