A, B and C can do a piece of work in 20,24 and 30 days respectively. They undertook to do the piece of work for 5,400. They begin the work together, but B left 2 days before the completion of work and C left 5 days before the completion of work. The share of A from the assured money is

Given A, B and C can do a piece of work in 20,24 and 30 days respectively

Let the work be completed in $$x$$ days

$$\Rightarrow \frac{x}{20} + \frac{x - 2}{24} + \frac{x - 5}{30} = 1$$

$$\Rightarrow \frac{6x + 5(x -2) + 4(x - 5)}{120} = 1$$

$$\Rightarrow \frac{6x + 5x -10 + 4x - 20}{120} = 1$$

$$\Rightarrow 6x + 5x + 4x = 120 + 30$$

$$\Rightarrow 15x = 150 \Rightarrow x = 10$$

Work done by A,

$$\frac{10}{20} \times 5400 = 2700$$

Hence, option A is the correct answer.