Time and work Quantitative aptitude question

[Q] A alone can do a piece of work in 6 days and B alone can do it in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
(a) 400
(b) 200
(c) 300
(d) 100

Solution

Answer   (a)
Explanation
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Amount of work A can do in 1 day = 1/6

Amount of work B can do in 1 day = 1/8

Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24

Amount of work A + B + C can do = 1/3

Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24

work A can do in 1 day: work B can do in 1 day: work C can do in 1 day

= 1/6 : 1/8 : 1/24 = 4 : 3 : 1

Amount to be paid to C = 3200 × (1/8) = 400