Question

Three persons named John, David and Robert, are hired to complete a piece of work John alone takes 8 days, David alone takes 12 days and Robert alone takes 16 days to complete the work. To start with, John works for 2 days and is then replaced by David. David works for 3 days and then replaced by Robert to complete the remaining work. If the total wages of John, David and Robert are $3000. then find johns wages for his work.
a. 850
b. 600
c. 900
d. 750​

Answer 1

The wage John receives for his work is 750.

Given:

John completers the work alone in 8 days.

David completers the work alone in 12 days.

Robert completers the work alone in 16 days.

Total wage is 3000.

Explanation:

Let the total work done be 1.

Work completed by John in 1 day is 1/8.

Work completed by David in 1 day is 1/12.

Work completed by Robert in 1 day is 1/16.

Let the remaining work done by Robert is 'x'.

Total work done by all is,

$\frac{1}{8}$×$2$ + $\frac{1}{12}$×$3$ + $x$ = $1$

Solving above equation,

x = $\frac{1}{2}$

Therefore, the work done by john is 25%.

The work done by David is also 25%.

The work done by Robert is 50%.

wage earned by John is 25% of 3000 = 750.

Thus, the wage earned by John is 750.

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