Question

16 men can build a wall in 25 days . How many days will 20 men take to build the same wall ?

Answer 1

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

Given that,

• 16 men can build a wall in 25 days.

Now, we have to find in how many days, will 20 men build the same wall.

As, more men are there, so less days will be taken to build the wall.

So, it means, number of men and number of days are in inverse variation, i.e. More men, less number of days.

Let assume that 20 men take x days to build the wall.

So,

$\\ \begin{array}{|c|c|c|c} \hline \rm Number \: of \: men&\rm 16&\rm 20 \\ \hline\rm Number \: of \: days&\rm 25&\rm x \\ \hline \end{array}$

By using inverse variation, we have

$\rm \: 16 \times 25 = 20 \times x$

$\rm\implies \:x = 20 \: days$

So, 20 days taken by 20 men to build the wall.

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

Basic Concept :-

Inverse Variation :- Two quantities x and y are said to be in inverse variation if x increases then y decreases or if x decreases then y increases.

Answer 2

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

$\large\underline{\sf{given: according \:to \: the \: question }}$

$\large\underline{\sf{16men \: can \: build \: a \: wall \: in \: 25 \: days}}$

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$\large\underline{\sf{to \: find:in \: how \: many \: days}}$

$\large\underline{\sf{20men \: will \: build \: the \: wall.}}$

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$\large\purple{\sf{before \: we \: start \: we \: know \: that}}$

$\large\purple{\sf{the \: work \: is \: in \: { \red{ \: indirect \: variation}}}}$

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$\large\underline{\sf{we \: know \: that \: formula \: for}}$

$\large\red{\sf{indirect \: variation \: is \downarrow}}$

$\large\green{\sf{ \frac{x_{1}}{ x_{2} } = \frac{y_{1}}{ y_{2}} }}$

$\large\green{\sf{ \implies x_{1} \times y_{2} = y_{1} \times x_{2}}}$

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$\large\underline{\sf{putting \: the \: values \: we \: get}}$

$\frac{16 \times 25}{20} = 20$

OR

$16 \times 25 = 20 \times y$

$\implies \frac{16 \times 25}{20}$

$\implies 20days$

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