A can do piece of work in 8 days which B can destroy in 3 days A has worked for 6 days during the la...........

Quant (SSC) Time and work

A can do piece of work in 8 days which B can destroy in 3 days. A has worked for 6 days, during the last 2 days of which B has been destroying. How many days must A now work alone to complete the work?

7 days

7 2/3 days

7 1/3 days

8 days

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Explanation:

A's 1 day's efficiency = 1/8
B's 1 day's efficiency = -1/3
Let's assume A takes x more days to complete the work.
The equation will be like
= (6 + x) /8 - 2/3 = 1
= (6 + x) /8 = 1 + 2/3 = 5/3
⇒ 3(6 + x) = 40
⇒ 18 + 3x = 40
⇒ 3x = 22
∴ x = 22/3 = 7 1/3 days