Question

8. Twelve men can do a piece of work in 15 days.
How many men are required to complete a work
which is three and a half times the original work
in 10 days?
(a) 18
(b) 54
(c) 63
(d) 70​

Answer 1

Assume each person has the same efficiency.

At a constant time interval, as the no. of men increases the amount of work to be done also increases, i.e., both are directly proportional.

$\longrightarrow m\propto w\quad\quad\dots(1)$

The time needed to complete a constant amount of work decreases as the no. of men increases, i.e., both are inversely proportional.

$\longrightarrow m\propto \dfrac{1}{t}\quad\quad\dots(2)$

Combining (1) and (2), we get,

$\longrightarrow m\propto \dfrac{w}{t}$

$\Longrightarrow\dfrac{mt}{w}=constant$

$\Longrightarrow\dfrac{m_1t_1}{w_1}=\dfrac{m_2t_2}{w_2}$

$\longrightarrow m_2=\dfrac{m_1t_1w_2}{w_1t_2}\quad\quad\dots(3)$

Here 12 men can do a piece of work in 15 days.

• $m_1=12$

• $t_1=15$

The new work to be done is three and a half times the original work.

• $w_2=3\,\dfrac{1}{2}\ w_1$

• $w_2=\dfrac{7w_1}{2}$

We're asked to find out no. of men required to complete this work in 10 days.

• $t_2=10$

From (3),

$\longrightarrow m_2=\dfrac{12\times 15\times \dfrac{7w_1}{2}}{w_1\times10}$

$\longrightarrow\underline{\underline{m_2=63}}$

Therefore, 63 men are required.

Answer 2

Answer:

option c) 63 mens is the correct a answer