Question

A can do a piece of work in 6 days while B alone can do it in 8 days. With the help of C, they can complete the work in 2 days. If they are paid Rupees 720 for the whole work, how much money A gets?

• A. Rupees 180
• B. Rupees 240
• C. Rupees 300
• D. Rupees 420

Hint:

In work and wages problems, always reduce the data to "1-day work" (or unit work). Then compare each person’s contribution over the total period and divide wages in the same ratio.

Answer 1

The Correct Option is B

Step 1: Work rates of A and B
A completes the work in 6 days. Hence, A’s 1-day work = \( \frac{1}{6} \).
B completes the work in 8 days. Hence, B’s 1-day work = \( \frac{1}{8} \).
Step 2: Combined rate of A, B, and C
Together, A, B, and C complete the work in 2 days. Hence, their combined 1-day work = \( \frac{1}{2} \).
Step 3: Finding C’s rate
\[ \frac{1}{6} + \frac{1}{8} + \text{C’s 1-day work} = \frac{1}{2} \]
Take LCM of 6 and 8, which is 24:
\[ \frac{4}{24} + \frac{3}{24} + \text{C’s 1-day work} = \frac{1}{2} \]
\[ \frac{7}{24} + \text{C’s 1-day work} = \frac{1}{2} \]
\[ \text{C’s 1-day work} = \frac{1}{2} - \frac{7}{24} = \frac{12}{24} - \frac{7}{24} = \frac{5}{24} \]
Step 4: Work done individually in 2 days
- Work done by A in 2 days = \( 2 \times \frac{1}{6} = \frac{2}{6} = \frac{1}{3} \).
- Work done by B in 2 days = \( 2 \times \frac{1}{8} = \frac{2}{8} = \frac{1}{4} \).
- Work done by C in 2 days = \( 2 \times \frac{5}{24} = \frac{10}{24} = \frac{5}{12} \).
Check: \(\frac{1}{3} + \frac{1}{4} + \frac{5}{12} = \frac{4}{12} + \frac{3}{12} + \frac{5}{12} = 1 \). ✅
Step 5: Payment distribution
The total payment is distributed in the ratio of work done.
Work fractions = A : B : C = \( \frac{1}{3} : \frac{1}{4} : \frac{5}{12} \).
Take LCM of 12: \( \frac{4}{12} : \frac{3}{12} : \frac{5}{12} = 4 : 3 : 5 \).
Step 6: A’s share
Total ratio sum = \( 4 + 3 + 5 = 12 \).
A’s share = \( \frac{4}{12} \times 720 = \frac{1}{3} \times 720 = 240 \). ✅
\[ \boxed{240} \]