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

Correct Answer:
A) Rs.2700

Description for Correct answer:
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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