Question

A can do a piece of work in 10 days, B in 15 days. They work together for 5 days, the rest of the work is finished by C in two more days. If they get Rs.\ 3000 as wages for the whole work, what are the daily wages A, B and C respectively (in Rs.)?

• A. \(300, 200, 250\)
• B. \(200, 300, 250\)
• C. \(300, 200, 400\)
• D. \(300, 250, 500\)
• E. \(300, 400, 250\)

Answer 1

The Correct Option is A

Concept: Wages are proportional to
work done.
Step 1: Find rates.
\[ A = \frac{1}{10}, \quad B = \frac{1}{15} \] \[ A+B = \frac{1}{10} + \frac{1}{15} = \frac{1}{6} \]
Step 2: Work done in 5 days.
\[ 5 \times \frac{1}{6} = \frac{5}{6} \] Remaining work: \[ 1 - \frac{5}{6} = \frac{1}{6} \]
Step 3: Find C's rate.
\[ 2 \times \text{C's rate} = \frac{1}{6} \Rightarrow \text{C's rate} = \frac{1}{12} \]
Step 4: Total work shares.
\[ A = 5 \times \frac{1}{10} = \frac{1}{2} \] \[ B = 5 \times \frac{1}{15} = \frac{1}{3} \] \[ C = \frac{1}{6} \] \[ \text{Ratio} = \frac{1}{2} : \frac{1}{3} : \frac{1}{6} = 3 : 2 : 1 \]
Step 5: Divide wages.
\[ 3000 \div (3+2+1) = 500 \] \[ A = 1500,\quad B = 1000,\quad C = 500 \] Daily wages: \[ A = 300,\quad B = 200,\quad C = 250 \]
Step 6: Option analysis.

• (A) Correct \checkmark
• Others incorrect $\times$

Conclusion:
Thus, the correct answer is
Option (A).