Time & Work, General Mathematics

Question:A is twice as good a workman as B and together they finish a piece of work in 18 days. In how many days will A alone finish the work ? 
Answer(A's 1 day's work): (B's 1 day's work) = 2 : 1.

(A + B)'s 1 day's work `= 1/18`

Divide` 1/18` in the ratio 2 : 1.

:. A's 1 day's work` = (1/18 xx 2/3) = 1/27`

Hence, A alone can finish the work in 27 days.

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Question:A and B undertake to do a piece of work for Rs. 600. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they finish it in 3 days. Find the share of each. 
AnswerC,s 1 day's work` = 1/3 - (1/6 + 1/8) = 1/24`

:. A : B : C = Ratio of their 1 day's work

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

:. A's share `= Rs. (600 xx 4/8) = Rs. 300`

B's share `= Rs. (600 xx 3/8)`

    `= Rs, 225.`

C,s share = Rs. [600 - (300 + 225)]`

        `= Rs. 75`

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