Question

18 men can do a piece of work in 10 days. How many less men are required if the work is to be completed in 15 days? . A hostel had ration for 60​

Answer 1

Question :-

18 men can do a piece of work in 10 days. How many less men are required, if the work is to be completed in 15 days ?

$\large\underline{\sf{Solution-}}$

Given that,

18 men can do a piece of work in 10 days.

Now, we have to find, how many less men are required if the work is to be completed in 15 days.

Let suppose that x less men are required.

So, it means 18 men can do a piece of work in 10 days and 18 - x men can completed the work in 15 days.

As, less men do a piece of work, so more days are needed to complete the work.

It means, number of days and number of men are inverse variation..

So,

$\begin{array}{|c|c|c|c} \hline \rm Number \: of \: men&\rm 18&\rm 18 - x \\ \hline\rm Number \: of \: days&\rm 10&\rm 15 \\ \hline \end{array}$

So, using law of inverse variation, we have

$\rm \: 18 \times 10 = (18 - x) \times 15$

$\rm \: 180 = (18 - x) \times 15$

$\rm \: 18 - x = \dfrac{180}{15}$

$\rm \: 18 - x = 12$

$\rm \: - x = 12 - 18$

$\rm \: - x = - 6$

$\rm\implies \:x = 6$

So, it means 6 men less are required to complete the work in 15 days.

$\rule{190pt}{2pt}$

Basic Concept Used :-

Inverse Variation :- Two variables x and y are said to be in inverse or indirect Variation, if there is increase in x, then there is decrease in y or if there is decrease in x, then there is increase in y.