Arun, Varun and Tarun, if working alone, can complete a task in 24, 21, and 15 days, respectively. They charge Rs 2160, Rs 2400, and Rs 2160 per day, respectively, even if they are employed for a partial day. On any given day, any of the workers may or may not be employed to work. If the task needs to be completed in 10 days or less, then the minimum possible amount, in rupees, required to be paid for the entire task is

Let's assume that Total work = 1

If the work is entirely carried by each one of them it would cost 

Arun: $$2160 \times 24 = 51840$$

Varun: $$2400 \times 21 = 50400$$

Tarun: $$2160 \times 15 = 32400$$

The cheapest worker is Tarun. He can finish the work in 15 days. But we need the work completed in 10 days.

Tarun does $$10 \times \frac{1}{15} = \frac{2}{3}$$

$$1 - \frac{2}{3} = \frac{1}{3}$$

Complete the remaining (1/3) work using the next cheapest worker, which is Varun.

Days needed: $$\frac{x}{21} = \frac{1}{3} \quad\Rightarrow\quad x = 7$$

Total cost = Amount paid for Tarun + Amount paid for Varun = $$10 \times 2160 + 7 \times 2400 = 38400$$