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 will be how much?

• A. 400
• B. 450
• C. 100
• D. 333
• E. 300

Hint:

When payment is proportional to work, find the ratio of their work contributions over the given time. This ratio directly determines the share of the total payment.

Answer 1

The Correct Option is C

Step 1: Find Individual Work Rates:
Let total work = 1 unit. Amal's rate: $A = \frac{1}{10}$ per day. Bimal's rate: $B = \frac{1}{8}$ per day. Let Kamal's rate = $K$ per day.
Step 2: Find Kamal's Rate:
All three together complete work in 4 days: $(A+B+K) \times 4 = 1$. $A+B+K = \frac{1}{4}$. $\frac{1}{10} + \frac{1}{8} + K = \frac{1}{4}$. $\frac{4+5}{40} + K = \frac{1}{4}$. $\frac{9}{40} + K = \frac{1}{4} = \frac{10}{40}$. $K = \frac{1}{40}$ per day.
Step 3: Find Ratio of Work Done:
In 4 days, work done by each: Amal: $4 \times \frac{1}{10} = \frac{4}{10} = \frac{2}{5} = 0.4$. Bimal: $4 \times \frac{1}{8} = \frac{4}{8} = \frac{1}{2} = 0.5$. Kamal: $4 \times \frac{1}{40} = \frac{4}{40} = \frac{1}{10} = 0.1$. Ratio of work = $0.4 : 0.5 : 0.1 = 4 : 5 : 1$.
Step 4: Share the Remuneration:
Total parts = $4+5+1=10$. Kamal's share = $\frac{1}{10} \times 1000 = \text{Rs. } 100$.
Step 5: Final Answer:
Kamal's share is Rs. 100.