Question

Sohan can do a piece of work in 16 days and
Rohan in 24 days. They take the help of Mohan
and three together finish the work in 6 days.
If total remuneration for the work is 80, then
amount each will receive in proposition to the
work done by each is?​

Answer 1

Sohan got Rs 30 and rohan got Rs 20 and mohan got Rs 30

Solution:

Given that,

Sohan can do a piece of work in 16 days and  Rohan in 24 days

They take the help of Mohan  and three together finish the work in 6 days

Find the days taken by Mohan

Let "x" be the days taken by Mohan

$\frac{1}{16} + \frac{1}{24} + \frac{1}{x} = \frac{1}{6}\\\\\frac{1 \times 3}{16 \times 3} + \frac{1 \times 2}{24 \times 2} + \frac{1}{x} = \frac{1}{6}\\\\\frac{5}{48} + \frac{1}{x} = \frac{1}{6}\\\\\frac{1}{x} = \frac{1}{6} - \frac{5}{48}\\\\\frac{1}{x} = \frac{3}{48}\\\\x = 16$

Therefore,

Mohan can do a piece of work in 16 days

Sohan can do a piece of work in 16 days

Rohan in 24 days

They work in the ratio as:

Sohan : Rohan : Mohan

$Work\ efficiency = \frac{1}{16} : \frac{1}{24} : \frac{1}{16}\\\\Work\ efficiency = 3 : 2 : 3$

Let the work efficiency of sohan be 3x

Let the work efficiency of rohan be 2x

Let the work efficiency of mohan be 3x

Total remuneration for the work is 80

Therefore,

3x + 2x + 3x = 80

8x = 80

x = 10

Thus,

Amount received by Sohan = 3x = 3(10) = 30

Amount received by Rohan = 2x = 2(10) = 20

Amount received by Mohan = 3x = 3(10) = 30

Thus sohan got Rs 30 and rohan got Rs 20 and mohan got Rs 30

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