Question

10 men can lay a 75 km long road in 5 days. In how many days can 15 men lay a 45 km long road?
[3 marks]
[APSCERT- Ex 10.4 Q2]
[Compound Proportion]

Answer 1

Solution:
$$\begin{array}{ccc}No.ofworkers& Lengthofroad& No.ofdays\\ 10& 75& 5\\ 15& 45& x\end{array}$$
Here,
Length of the road($l$) ∝ Number of workers($n$)
Also, Length of road($l$) ∝ Number of days(𝒕)
$\therefore l\propto nt$
⇒ $\frac{l_1}{n_1\times t_1}=\frac{l_2}{n_2\times t_2}$
[1 mark]

⇒ $\frac{75}{10\times 5}=\frac{45}{15\times x}$

⇒ $x=\frac{45\times 10\times 5}{15\times 75}$

$\therefore$ $x=2days$

Hence, 2 days will be needed to lay a 45 km long road by 15 men.
[2 marks]