Question

Amal can complete a job in 10 days and Bimal can complete it in 8 days. Amal, Bimal and Kamal together complete the job in 4 days and are paid a total amount of Rs 1000 as remuneration.If this amount is shared by them in proportion to their work,then Kamal's share,in rupees,is

• A. 100
• B. 200
• C. 300
• D. 400

Answer 1

The Correct Option is A

To determine Kamal's share of the remuneration, we first need to understand how the work is distributed among Amal, Bimal, and Kamal based on their work rates.

1. Calculate individual work rates:
a. Amal can complete the job in 10 days, so his work rate is \( \frac{1}{10} \) of the job per day. 
b. Bimal can complete the job in 8 days, so his work rate is \( \frac{1}{8} \) of the job per day.

2. When working together, Amal, Bimal, and Kamal complete the job in 4 days, meaning their combined work rate is \( \frac{1}{4} \) of the job per day.

3. Set up the equation representing the combined work rate:
\[ \frac{1}{10} + \frac{1}{8} + \frac{1}{k} = \frac{1}{4} \]
where \( \frac{1}{k} \) is Kamal's work rate.

4. Solve for \( \frac{1}{k} \):
a. Find the sum of Amal's and Bimal's work rates:
\[ \frac{1}{10} + \frac{1}{8} = \frac{4}{40} + \frac{5}{40} = \frac{9}{40} \]
b. Subtract their combined rate from the total combined rate:
\[ \frac{1}{4} - \frac{9}{40} = \frac{10}{40} - \frac{9}{40} = \frac{1}{40} \]
c. Thus, Kamal's work rate is \( \frac{1}{40} \).

5. Determine the proportion of work done by Kamal:
a. The total work done by Amal in 4 days is \( 4 \times \frac{1}{10} = \frac{4}{10} = \frac{2}{5} \).
b. The work done by Bimal is \( 4 \times \frac{1}{8} = \frac{4}{8} = \frac{1}{2} \).
c. The work done by Kamal is \( 4 \times \frac{1}{40} = \frac{4}{40} = \frac{1}{10} \).

6. Calculate each person's share:
a. Total work done is \( \frac{2}{5} + \frac{1}{2} + \frac{1}{10} = 1 \) (as expected).
b. Kamal's share of the total remuneration based on his fraction of the total work:
\[ \text{Kamal's share} = 1000 \times \frac{1}{10} = 100 \]

Thus, Kamal's share is Rs 100.