$$A_1$$ alone can complete a piece of work in 14 days, $$A_2$$ alone can complete the same work in 21 days, while $$A_3$$ alone can complete the same work in 28 days. The three worked together, completed the work, and received a total payment of ₹1,040 for doing the work. What is $$A_2$$ 's share in the total payment received?

Let's assume the total work is 84 units.

$$A_1$$ alone can complete a piece of work in 14 days.

Efficiency of $$A_1$$ = $$\frac{84}{14}$$ = 6 units/day

$$A_2$$ alone can complete the same work in 21 days.

Efficiency of $$A_2$$ = $$\frac{84}{21}$$ = 4 units/day

While $$A_3$$ alone can complete the same work in 28 days.

Efficiency of $$A_3$$ = $$\frac{84}{28}$$ = 3 units/day

The three worked together, completed the work, and received a total payment of ₹1,040 for doing the work.

As we know that the money will be distributed among them as per their efficiencies.

The share of $$A_2$$ in the total payment received = $$\frac{1040}{\left(6+4+3\right)}\times4$$

= $$\frac{1040}{13}\times4$$

= $$80\times4$$

= ₹320