• 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 Rs.5400. 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
 A) Rs.2700 B) Rs.540 C) Rs.1800 D) Rs.600

 A) Rs.2700

Let the number of days to complete the work be x.

According to the question,

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

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

= $$\Large 6x +5x+4x = 120+10+20$$

= 15x = 150

Therefore, x = 10

Therefore, Work done by A = $$\Large \frac{10}{20} = \frac{1}{2}$$

Therefore, Share of A from the assured money = $$\Large \frac{1}{2} \times 5400$$ = Rs.2700

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