A can do a piece of work in 12 days while B alone can do it in 15 days. With the help of C they can finish the work in 5 days. If they are paid ₹960 for the whole work, how much money A gets?

Correct option is D

We are tasked to calculate how much money A gets from the total payment of ₹960 for completing a piece of work with B and C .

Step-by-Step Solution:

1. Given:

- A can complete the work in 12 days.

- B can complete the work in 15 days.

- Together with C , they finish the work in 5 days.

- Total payment is ₹960.

2. Work rates:

- Work done by A in 1 day = $$\frac{1}{12}$$​ 

- Work done by B in 1 day = $$\frac{1}{15}$$​ 

- Together with C , work done in 1 day = $$\frac{1}{5}$$​​

3. Work done by C in 1 day:

Total work done by A, B, C in 1 day:

​$$\frac{1}{5}$$​

Work done by A and B in 1 day:

​$$\frac{1}{12} + \frac{1}{15} = \frac{5}{60} + \frac{4}{60} = \frac{9}{60} = \frac{3}{20}$$​

Work done by C in 1 day:

​$$\frac{1}{5} - \frac{3}{20} = \frac{4}{20} - \frac{3}{20} = \frac{1}{20}$$​

4. Share of work completed by each:

Total work = 1 (the whole piece of work).

- Work completed by A :

​$$5 \times \frac{1}{12} = \frac{5}{12}$$​

- Work completed by B :

​$$5 \times \frac{1}{15} = \frac{5}{15} = \frac{1}{3}$$​

- Work completed by C :

​$$5 \times \frac{1}{20} = \frac{5}{20} = \frac{1}{4}$$​

5. Divide payment based on work done:

The total payment of ₹960 is divided in the ratio of the work done:

Ratio of work done by  A : B : C = $$\frac{5}{12} : \frac{1}{3} : \frac{1}{4}$$​

Convert to a common denominator:

​$$\frac{5}{12} = \frac{20}{48}, \quad \frac{1}{3} = \frac{16}{48}, \quad \frac{1}{4} = \frac{12}{48}$$​

Ratio of work:

20 : 16 : 12

6. Total parts and share of A :

Total parts = 20 + 16 + 12 = 48 .

- A 's share:

​$$\frac{20}{48} \times 960 = \frac{19200}{48} = ₹400$$​

Final Answer:

​$$\boxed{₹400}$$​