A alone can finish a job in 12 days, while B alone can finish it in 15 days. With the help of C, they can finish the same job in 5 days. If they are paid ₹2,880 for the whole job, what will be the share of C?

Correct option is D

Given:
A can finish the job in 12 days.
B can finish the job in 15 days.
A, B, and C together can finish the job in 5 days.
Total payment for the job is ₹2,880.

Solution:
A's efficiency $$= \frac{1}{12}$$ (job/day).

B's efficiency =$$\frac{1}{15}$$​(job/day).
Combined efficiency of A, B, and C=$$\frac{1}{5}$$​ (job/day).
Let C's efficiency be $$\frac{1}{x} .$$​Then:
​$$\frac{1}{12} + \frac{1}{15} + \frac{1}{x} = \frac{1}{5}$$​

$$\frac{5}{60} + \frac{4}{60} + \frac{1}{x} = \frac{12}{60}$$​

$$\frac{9}{60} + \frac{1}{x} = \frac{12}{60}$$​

$$\frac{1}{x} = \frac{12}{60} - \frac{9}{60} = \frac{3}{60} = \frac{1}{20}$$​

Thus, C's efficiency $$\frac{1}{20}$$​ (job/day).
A's contribution in 5 days:  5$$\times \frac{1}{12} = \frac{5}{12}$$​​

B's contribution in 5 days:  5$$\times \frac{1}{15} = \frac{1}{3} = \frac{4}{12}$$​

C's contribution in 5 days:  5$$\times \frac{1}{20} = \frac{1}{4} = \frac{3}{12}$$​​
The ratio of contributions is:
​$$\frac{5}{12} : \frac{4}{12} : \frac{3}{12} = 5 : 4 : 3$$​​
Total parts = 5 + 4 + 3 = 12 
C's share =$$\frac{3}{12} \times 2880 = ₹720$$

Alternate Method:

Efficiency of C = 12 - 9 = 3 

C's share =$$\frac{3}{12} \times 2880 = ₹720$$​
​