Three persons started to complete a project for Rs. 1,600. The first person can complete the project in 8 days, the second person in 12 days and the third person in 16 days. They complete the project together with the help of a fourth person in 3 days.

Three persons started to complete a project for Rs. 1,600. The first person can complete the project in 8 days, the second person in 12 days and the third person in 16 days. They complete the project together with the help of a fourth person in 3 days. What will the fourth person get?
1). Rs. 280
2). Rs. 300
3). Rs. 325
4). Rs. 250

First person does the work in 8 days

∴ part of work done in one day by first person = 1/8

First person does the work in 12 days

∴ part of work done in one day by second person = 1/12

First person does the work in 16 days

∴ part of work done in one day by third person = 1/16

part of work done in one day by all three persons together $(= \;\frac{1}{8} + \frac{1}{{12}} + \frac{1}{{16}} = \frac{{6 + 4 + 3}}{{48}} = \frac{{13}}{{48}})$

Let the number of days needed by the fourth person to finish the work alone be x,

So the part of work done by fourth person in one day = 1/x

When all four of them work together, they finish the work in 3 days.

∴ part of work done by all four of them together = 1/3

$(\begin{array}{l} \Rightarrow \;\frac{{13}}{{48}} + \frac{1}{x} = \frac{1}{3}\\ \Rightarrow \frac{1}{x} = \frac{1}{3} - \frac{{13}}{{48}}\\ \Rightarrow \;\frac{1}{x}\; = \;\frac{{16 - 13}}{{48}}\; = \;\frac{3}{{48}}\; = \;\frac{1}{{16}} \end{array})$

∴ fourth person will finish the project in 16 days

Now, comparing efficiencies of all the four persons to finish the project = $(\frac{1}{8}:\frac{1}{{12}}:\frac{1}{{16}}:\frac{1}{{16}} = 6\;:4\;:3\;:3)$

Thus, amount that fourth person will get $(= \frac{3}{{6 + 4 + 3 + 3}} \times 1600 = \;\frac{3}{{16}} \times 1600 = Rs.\;300)$

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