Question : A and B undertake a project worth Rs. 36,000. A alone can do the work in 25 days. They worked together for 5 days. For the next five days, B worked alone. After that, A substituted B and completed the remaining work in 5 days. The share of A in the earnings is:
Option 1: Rs. 14,400
Option 2: Rs. 21,400
Option 3: Rs. 14,600
Option 4: Rs. 21,600
Correct Answer: Rs. 14,400
Solution :
A can complete the work in 25 days, so A's work rate is $\frac{1}{25}$ of the work per day.
They worked together for 5 days, so they completed $5 \times \frac{1}{25} = \frac{1}{5}$ of the work.
For the next five days, B worked alone.
Let B complete the b part of the work.
After that, A substituted B and completed the remaining work in 5 days.
So, A completed another $5 \times \frac{1}{25} = \frac{1}{5}$ of the work.
So, the total work done is 1 (as the project is completed).
$⇒\frac{1}{5} + b + \frac{1}{5} = 1$
$⇒b=\frac{3}{5}$
This means B completed $\frac{3}{5}$ of the work, and A completed $\frac{2}{5}$ of the work.
The earnings are divided according to the proportion of work done.
So, A's share of the earnings is $\left(\frac{2}{5}\right)$ × Rs. 36,000 = Rs. 14,400
Hence, the correct answer is Rs. 14,400.
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