Question

A, B and C can do a work in 6, 8 and 12 days respectively. If they do the work together and earn Rs. 2700, what is the share of C in that amount?

• A. 600
• B. 900
• C. 1000
• D. 700

Hint:

The share ratio equals the daily-work-rate ratio: 4:3:2.

Answer 1

The Correct Option is A

To determine C's share when A, B, and C work together to complete a task and earn Rs. 2700, we need to find how the work contribution from each affects their respective earnings. 

Step 1: Determine Work Contribution of Each Individual

First, determine the work rate of each individual:

• A can complete the work in 6 days. So, A's one day's work is \(\frac{1}{6}\).
• B can complete the work in 8 days. So, B's one day's work is \(\frac{1}{8}\).
• C can complete the work in 12 days. So, C's one day's work is \(\frac{1}{12}\).

Step 2: Calculate Total Work Per Day When All Work Together

Their combined one day's work is:

\(\frac{1}{6} + \frac{1}{8} + \frac{1}{12}.\)

Find the least common multiple of 6, 8, and 12, which is 24 and compute:

\(\frac{4}{24} + \frac{3}{24} + \frac{2}{24} = \frac{9}{24} = \frac{3}{8}.\)

Step 3: Determine Individual Contribution to Total Earnings

The share of each individual is proportional to their work possibly to total work:

• A's share: \(\frac{4}{9}\) parts
• B's share: \(\frac{3}{9}\) parts
• C's share: \(\frac{2}{9}\) parts

Step 4: Calculate C's Earnings

The total earnings are Rs. 2700. So, C's share is:

\(\frac{2}{9} \times 2700\), which equals Rs. 600.

Conclusion

Therefore, the share of C in the amount is Rs. 600.

Answer 2

Step 1: Convert the days into daily work rates using the LCM.
Take the total work as \(\text{LCM}(6,8,12) = 24\) units. Then A does \(24/6 = 4\) units a day, B does \(24/8 = 3\) units a day, and C does \(24/12 = 2\) units a day.

Step 2: Money is shared in the same ratio as the work each person did.
Since they work together for the same number of days, the ratio of their shares equals the ratio of their daily rates: \(4:3:2\), which adds up to 9 parts in total.

Step 3: Find C's share out of Rs. 2700.
C's part is 2 out of 9 parts, so:
\[ \text{C's share} = \frac{2}{9} \times 2700 = 600 \]

Final Answer:
C receives Rs. 600 out of the total earnings.
\[ \boxed{600} \]