Question : A and B together can complete a project in 30 days. They started together, but after 6 days, A left the work and the work was completed by B after 36 more days. Single person A can complete the entire work in how many days?
Option 1: 45 days
Option 2: 90 days
Option 3: 60 days
Option 4: 120 days
Correct Answer: 90 days
Solution : Given: A and B together can complete a project in 30 days. They started together, but after 6 days, A left the work, and the work was completed by B after 36 more days. We know the formula, Work = Efficiency × Time Let the efficiency of A and B be $a$ and $b$ respectively. According to the question, $30\times(a+b)=6\times(a+b)+36b$ ⇒ $24(a+b)=36b$ ⇒ $24a=36b–24b$ ⇒ $24a=12b$ ⇒ $2a=b$ Let $a=1$ unit and $b=2$ units Total work = 1 + 2 = 3 units So, work done is 30 × 3 = 90 units. The time taken by A alone to do the work is $\frac{90}{1}$ = 90 days Hence, the correct answer is 90 days
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