Question

A is thrice as fast as b. If a takes 60 days less than b to complete a piece of work, find the number of days it would take to complete the work if both work together with a at 4/3 and b at 3/2 of their original efficiency

Answer 1

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Implication & Assumption:

If A is thrice as good as B, then there are 2 implications:

i) A shall be able to do three times the work done by B in the same time. So let's say if B produces 1 unit in a day, A will produce 3 units

ii) A must be able to finish the same job in one-third of the time taken by B. So let's say if A takes X days to complete the work, B will do it in 3X days

Working:

Since A finishes the job in 60 days less, from (ii) we get: 3X - X = 60

So, X = 30 (A finishes the work in 30 days and B in 90 days)

Now from (i), since A produces 3 units per day in 30 days he must produce 90 Units (same way, B shall produce 90 units in 90 days)

Thus, total Work = 90 units

Final Step:

When working together, A & B will jointly produce 4 units per day. So to make 90 units they will need 90/4 = 22.5 day

Thus they will complete the work in 22.5 days (Answer).

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