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A and B can finish a work in 2.4 days. If the number of days for which they work increases by 2 days each for A and B then time taken by them together to finish the work is 24/7 days. Find the time taken by them to complete the work together, If the number of days for which they work increases by 4 days each?

A and B can finish a work in 2.4 days. If the number of days for which they work increases by 2 days each for A and B then time taken by them together to finish the work is 24/7 days. Find the time taken by them to complete the work together, If the number of days for which they work increases by 4 days each? Correct Answer 40/9

Given:

A and B can finish a work in 2.4 days.

Formula used:

Time taken by A and B to together finish a work which they alone finish in ‘a’ and ‘b’ days respectively is a × b/(a + b)

Calculation:

Let ‘A’ is the work done by A in a day and ‘B’ is the work done by B in a day

⇒ Let total work = 24 units, multiple of 2.4 (any value as it will not affect the answer)

Work done by both in a day = 24/2.4 = 10 units

⇒ A + B = 10

Let A = 4 units and B = 6 units if we take reverse then also it will not affect the answer

So, A alone can complete = 24/4 = 6 days and for B = 24/6 = 4 days

If each of them takes 2 days more

⇒ A = 6 + 2 = 8 days and B = 6 days

Now, A = 24/8 = 3 units and B = 24/6 = 4 units

⇒ A + B = 4 + 3 = 7 units, Total time = 24/7 satisfies condition

Now, both takes 4 days more each

⇒ A can complete in 6 + 4 = 10 days

⇒ and B in 4 + 4 = 8 days

∴ Required time = 10 × 8/(10 + 8) = 80/18 = 40/9 days

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