Q) A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?

a) 11 days                             b) 13 days              

c) 20 3/17 days                     d) None of these

Ans:

A does the work in 23 days

∴ Work done by A in 1 day = 1/23

Since A is 30% more efficient than B, therefore A will do 1.3 times work as done by B or A will take 1/1.3 time of time taken by B.

∴ If A does 1/23 work in one day, B will do 1/23 x 1/1.3 work in one day (A = 1.3 B or B = A/1.3)

∴ Work done by (A + B) together in 1 day

= 1/23 + 1/23 x 1/1.3 = 1/23 (1+1/1.3) = 1/23 (2.3/1.3) = 23/13 x 1/23 = 1/13

Since time taken by (A + B) together to do 1/13 work = 1 day

∴ Time taken by (A + B) to finish the full work together = 1(1/13) = 13 days

Hence, Answer is [B].

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