A can do a piece of work in 12 days while B alone can do it in 15 days. With the help of C they can finish it in 5 days. If they are paid Rs. 960 for the whole work. How much money A gets ?
A. Rs. 480
B. Rs. 240
C. Rs. 320
D. Rs. 400
Answer: Option D
Solution(By Examveda Team)
(A + B)'s 1 day work$$\eqalign{ & = \frac{1}{{12}} + \frac{1}{{15}} \cr & = \frac{{5 + 4}}{{60}} \cr & = \frac{9}{{60}} = \frac{3}{{20}} \cr} $$
(A + B + C)'s 1 day work = $$\frac{1}{5}$$
∴ C's 1 day work
$$\eqalign{ & = \frac{1}{5} - \frac{3}{{20}} \cr & = \frac{{4 - 3}}{{20}} \cr & = \frac{1}{{20}} \cr} $$
Ratio of their work
$$\eqalign{ & = \frac{1}{{12}}:\frac{1}{{15}}:\frac{1}{{20}} \cr & = 5:4:3 \cr} $$
$$\eqalign{ & {\text{A's}}\,{\text{share}} = \frac{5}{{12}} \times 960 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}400 \cr} $$
Related Questions on Time and Work
A. 18 days
B. 24 days
C. 30 days
D. 40 days
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