# How many days?

## Dec 1, 2017

20

#### Explanation:

Updated:
So the job takes 360 man-days to complete.
360/15=24 days
18 men would need to complete it in 360/18 or 20 days.

Or

$15 \cdot 24 = 18 \cdot \mathrm{da} y s$

$360 = 18 \mathrm{da} y s$

$20 = \mathrm{da} y s$

Dec 2, 2017

We can clearly see that this is an inverse proportion question, in that case, the rule is,
${x}_{1} \times {y}_{1} = {x}_{2} \times {y}_{2}$
Here, let ${x}_{1}$ be electricians, in the first case the number of electricians are 15, and the date(${y}_{1}$) is 24
Here, ${x}_{2}$ is 18, and ${y}_{2}$ is unknown. So,
$15 \times 24 = 18 \times {y}_{2}$
Divide both sides by 24
$\frac{15 \times \cancel{24}}{\cancel{24}} = \frac{{\cancel{18}}^{3} \times {y}_{2}}{{\cancel{24}}^{4}}$
We get
$15 = \frac{3 \times {y}_{2}}{4}$
Multiply both sides by 4
$15 \times 4 = \frac{3 \times {y}_{2}}{\cancel{4}} \times \cancel{4}$
We get
$60 = 3 \times {y}_{2}$
Divide both sides by 3
$\frac{{\cancel{60}}^{20}}{{\cancel{3}}^{1}} = {y}_{2}$
We get
$20 = {y}_{2}$
$\therefore 18$ electricians would require 20 days