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

A. 7 days

B. 7 1/3 days

C. 7 2/3 days

D. 8 days

Answer: Option B

Solution(By Examveda Team)

A can complete the work in 8 days.
Work rate of A = 100/8 = 12.5% per day.
B can destroy the work in 3 days.
Negative work rate of B = 100/3 = 33.33% per day.
Work completed by A in 6 days = 6 * 12.5 = 75%.
Now, B destroyed work in 2 days = 33.33 *2 = 66.66%.
Work undestroyed by B = 75 - 66.66 = 8.34%.
Now work has to be completed by A = 100 - 8.34 = 91.66%
Thus, time needed by A = 91.66/12.5 = 7.33 days.