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Time taken by A and B to complete a work is in the ratio 2 : 3. A alone worked for 5 days and left the work then B alone worked for 10 days on the same work, It is found than 70% of the work is completed. Find the time in which they together can complete the work.

Time taken by A and B to complete a work is in the ratio 2 : 3. A alone worked for 5 days and left the work then B alone worked for 10 days on the same work, It is found than 70% of the work is completed. Find the time in which they together can complete the work. Correct Answer 10 days

Ratio of time taken by A and B to complete a work = 2 ∶ 3

∴ Ratio of efficiency of A and B = 3 ∶ 2

Let, efficiency of A = 3x/day and efficiency of B = 2x/day

Let, quantity of total work = a

According to problem,

⇒ 5 × 3x + 10 × 2x = 0.7a

⇒ 0.7a = 35x

⇒ a = 50x

Let, they together do the work in = y days

⇒ y × (3x + 2x) = 50x

⇒ y = 50x/5x

⇒ y = 10

∴ They together will complete the work in = 10 days

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