Question

10 men can lay a road 75km long in 5 days in how many days can 15 men lay a road 45 km long by proportional method​

Answer 1

$\huge{\bf{\green{\mathfrak{Question:-}}}}$

• 10 men can lay a road 75km long in 5 days then, in how many days can 15 men lay a road 45 km long by proportional method?

$\huge {\bf{\orange{\mathfrak{Answer:-}}}}$

• $\textsf{10 men can lay a road of 75km in 5 days.}$

• $\sf{1\: man\: can\: lay\: \dfrac{75}{10} \: =\: 7.5km.}$

• $\textsf{15 men can lay a road of 45km.}$

• $\sf{1\: man \:can\: lay\: \dfrac{45}{15} \: =\: 3km.}$

• $\textsf{By proportionality method (or) Cross multiplication,}$

• $\textsf{7.5km\: ————— \: ⟩ \: 5 days}$

• $\textsf{3km\: ————— \: ⟩ \: x days}$

• $\sf{3 \: * \: 5 \: = \: 7.5 \: * \: x}$

• $\sf{x \: = \: \dfrac{15}{7.5}}$

• $\boxed{\sf{x \: = \: 2.}}$

$\huge{\bf{\red{\mathfrak{Conclusion:-}}}}$

• $\boxed{\therefore{\sf{15 \: men \: lay \: a \: road \: 45km \: in \: 2 \: days.}}}$

Answer 2

Given :-

If 10 men can lay a road 75km long in 5 days

To Find :-

Days can 15 men lay a road 45 km long

Solution :-

Here, it is already given that we have to use proportional method.

Let the days be x

Men 1/Men 2 = Day 1/Day 2 = Road 1/Road 2

10/15 = 5/x = 75/45

2/3 = 5/x = 15/9

2/3 = 5/x = 5/3

(2/3)/(5/3) = 5/x

2/3 $\times$ 3/5 = 5/x

2/5 = 5/x

2 $\times$ 5 = 5x

10 = 5x

x = 10/5

x = 2 days