Question

If 42 men working together can construct a road in 13 days how long will take to 39 men construct the road ??

Answer 1

$\; \star \; {\underline{\boxed{\pmb{\orange{\frak{ \; Given\; :- }}}}}}$

Case 1 :

Men = 42

Time taken = 13days

Case 2 :

Men = 39

Time taken = x

$\star \;{\underline{\boxed{\pmb{\red{\frak{ \; To \; Find \; :- }}}}}}$

➺ How long will it take if 39men construct the road= ?

$\; \star \; {\underline{\boxed{\pmb{\purple{\frak{ \; SolutioN \; :- }}}}}}$

$❒{\underline{\underline{\sf{ \; Calculating \: Value of x\;  \: : - }}}}$

${\longrightarrow \; {\sf{42 :13 =39:x }}} \;$

${\longrightarrow \; {\sf{ \dfrac{42 }{13}= \dfrac{39}{ x} }}} \;$

As in inverse proportions we know that

$\underbrace{ \rm \: \hookrightarrow x _{1}y_{1} = x_{2}y_{2}}$

${\longrightarrow \; {\sf{ 42 \times 13= 39 \times x}}} \;$

${\longrightarrow \; {\sf{ 42 \times 13= 39x}}} \;$

${\longrightarrow \; {\sf{ \dfrac{42 \times 13}{39} = x}}} \;$

${\longrightarrow \; {\sf{{14 \times 1} = x}}} \;$

${\; \longrightarrow \; {{ \pink{ \underline{ \boxed{ \frak{ x=14days}}}}}} }\;\red\bigstar$

$\begin{gathered} \\ \\ \end{gathered}$

$\therefore$Hence the road will get constructed in 14days

$\begin{gathered}\begin{gathered}\begin{gathered} \\ {\underline{\rule{300pt}{9pt}}} \end{gathered} \end{gathered}\end{gathered}$

Answer 2

Answer:

• 14 days

Step-by-step explanation:

Let required number of day is x

Clearly, the lesser number of men , number of days are in constant.

So , it is a case of inverse variation.

Now, According to the information

$\sf \rightarrow \: x _1y_1 = x_2y_2$

⟼ 42 × 13 = 39 × x

⟼ 42 × 13 = 39x

⟼ 42 × 13 / 39 = x

⟼ 14 = x

Thus, 39 Men construct road in 14 days. Ans.

Note→ Stay connected with the attachment.

_______________________________________________________________

♦ Extra Information

In case of inverse variation on increase in one quantity result decrease in the other quantity and vice- versa.

If the value of two quantities depend upon each other in such a way that are change in one quantity result in the change in other quantity then 2 quantity are to be in variation.

Inverse

• The more number of men the less time will be taken to finish the work.
• The less number of men the more time will be taken to finish the work.