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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