Question : A and B together can complete a project in 10 days. They started together, but A left after 2 days and the remaining work was completed by B in 12 days. In how many days can A complete the entire work while working alone?
Option 1: 15 days
Option 2: 20 days
Option 3: 30 days
Option 4: 45 days
Correct Answer: 30 days
Solution :
Given: A and B together can complete a project in 10 days.
Let the efficiency of A is $x$ and B is $y$ respectively.
Total work = Efficiency × Time
Total work is $(x+y)×10 = 10(x+y)$
They started together, but A left after 2 days and the remaining work was completed by B in 12 days.
$(x+y)×2 + y×12 = 10(x+y)$
⇒ $2x+2y+12y = 10x+10y$
⇒ $8x = 4y$
⇒ $\frac{x}{y} = \frac{4}{8} = \frac{1}{2}$
Then, the efficiency of A is 1 unit and the efficiency of B is 2 units.
Total work is $10(x+y) = 10(1+2) = 30$ units
Time taken by A to complete the whole work is $\frac{30}{1}$ = 30 days
Hence, the correct answer is 30 days.
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