$$K_{1}$$ can do a piece of work alone in 4 days, $$K_{2}$$ can do the same work alone in 8 days, while $$K_{3}$$ can do it alone in 32 days. They work together and complete the work, and receive a total of ₹3900 as payment for doing the work. What is the share of the person who received the maximum amount?

Let's assume the total work is 32 units.

$$K_{1}$$ can do a piece of work alone in 4 days.

Efficiency of $$K_{1}$$ = $$\frac{32}{4}$$ = 8 units/day

$$K_{2}$$ can do the same work alone in 8 days.

Efficiency of $$K_{2}$$ = $$\frac{32}{8}$$ = 4 units/day

while $$K_{3}$$ can do it alone in 32 days.

Efficiency of $$K_{3}$$ = $$\frac{32}{32}$$ = 1 unit/day

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

Here the efficiency of $$K_{1}$$ is the maximum. So he will receive the maximum amount.

 share of the person who received the maximum amount = $$\frac{3900}{\left(8+4+1\right)}\times\ 8$$

= $$\frac{3900}{13}\times\ 8$$

= $$300\times\ 8$$

= ₹2400