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Ramesh and Suresh undertaken to do a piece of work for ₹ 800. Ramesh alone can do it in 12 days, while Suresh alone can do it in 16 days. With the assistance of a boy, they finish it in 6 days. How should the money be divided?
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- Ramesh = ₹ 100, Suresh = ₹ 300 and boy = ₹ 400
- Ramesh = ₹ 200, Suresh = ₹ 200 and boy = ₹ 400
- Ramesh = ₹ 400, Suresh = ₹ 300 and boy = ₹ 100
- Ramesh = ₹ 300, Suresh = ₹ 400 and boy = ₹ 100
- None of the above
Correct Option: C
Ramesh's 1 day's work = 1/12
Suresh's 1 day's work = 1/16
(Ramesh + Suresh)'s 1 day work = (1/12) + (1/16)
= (16 + 12) / (12 x 16)
= 28/192
= 7/48
Given that, (Ramesh + Suresh + Boy)'s
1 day's work = 1/6
∴ Boy's 1 day's work = (1/6) - (7/48) = (8 - 7)/ 48 = 1/48
∴ Ramesh's share : Suresh's share : Boy's share = 1/12 : 1/16 : 1/48
= (8/96) : (6/96) : (2/96)
= 8 : 6 : 2
= 4 : 3 : 1
Let Ramesh's share be 4k , Suresh's share be 3k and boy's share be k.
According to the question,
4k + 3k + k = 800
8k = 800
∴ k = 800/8 = 100
∴ Ramesh's share = 4k = 4 x 100 = ₹ 400
Suresh's share = 3k = 3 x 100 = ₹ 300
Boy's share = k = ₹ 100
