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S, T and U can complete a work in 40, 48 and 60 days respectively. They received Rs 10800 to complete the work. They begin the work together but T left 2 days before the completion of the work and U left 5 days before the completion of the work. S has completed the remaining work alone. What is the share of S(in Rs) from total money?

S, T and U can complete a work in 40, 48 and 60 days respectively. They received Rs 10800 to complete the work. They begin the work together but T left 2 days before the completion of the work and U left 5 days before the completion of the work. S has completed the remaining work alone. What is the share of S(in Rs) from total money? Correct Answer 4860

S’s 1 day work = 1/40

T’s 1 day work = 1/48

U’s 1 day work = 1/60

Let the work be completed in ‘x’ days, such that S worked for all x days, T worked for (x - 2) days and U for (x - 5) days

⇒ x/40 + (x - 2)/48 + (x - 5)/60 = 1

⇒ 6x + 5(x - 2) + 4(x - 5) = 240

⇒ 6x + 5x - 10 + 4x - 20 = 240

⇒ 15x = 270

⇒ x = 270/15 = 18 days

Hence, ratio of their share = (18/40) ∶ (16/48) ∶ (13/60) = 27 ∶ 20 ∶ 13

Sum of ratios = 27 + 20 + 13 = 60

∴ S’s share = (27/60) × 10800 = Rs. 4860

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