Question

if 45 men can complete a work in 5 day how many days will be taken by 90 mens to finish it​

Answer 1

$\large\underline{\bold{Given \:Question - }}$

• If 45 men can complete a work in 5 day. In how many days will be taken by 90 mens to finish it?

$\large\underline{\bold{ANSWER-}}$

Given that

• 45 men can complete a work in 5 days.

• Let number of days taken by 90 men to finish the same work be 'x' days.

So,

• Its a concept of Indirect variation.

As,

• More men will work, less number of days to finish the work.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf number \: of \: men & \bf number \: of \: days \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 45 & \sf 5 \\ \\ \sf 90 & \sf x \end{array}} \\ \end{gathered}$

So,

• using the formula of Indirect variation, we get

$\rm :\longmapsto\:45 \times 5 = 90 \times x$

$\rm :\longmapsto\:x = \dfrac{45 \times 5}{90}$

$\rm :\longmapsto\:x = 2.5 \: days$

Additional Information :-

Variation in Mathematics

• “Variation” defines a concept that deals with variability in mathematics.

• Variation is defined by any change in some quantity due to change in another.

Here follows the most common kinds of variation.

Direct Variation

• If two variables A and B are so related that when A increases ( or decreases ) in a given ratio, B also increases ( or, decreases ) in the same ratio, then A is said to vary directly as B ( or, A is said to vary as B ). This is symbolically written as, A ∝ B (read as, ‘A varies as B’ ).

Inverse Variation

• A variable quantity A is said to vary inversely as another variable quantity B, when A varies as the reciprocal of B i.e., when A varies as 1/B

• Thus, if A varies inversely as B, we write A ∝ 1/B or, A = m ∙ (1/B) or, AB = m where’m (≠ 0) is the constant of variation. Hence, if one variable varies inversely as another, then the product of the corresponding values of the variables is constant.

• Conversely, if AB = k where A and B are variables and k is a constant, then A ∝ 1/B Hence, if the product of the corresponding values of two variables is constant, then one quantity varies inversely as another.