Question

A farmer has enough food to feed his family for 10 days. If 3 out of 8 members leave the house, then for how many days will the food last?

Answer 1

Given,
8 members can consume the food in 10 days.

We know that lesser the number of members in the family more will be the number of days for which the food will last.

$\text{So, Number of members}\left(x\right)\propto \frac{1}{\text{Number of days}\left(y\right)}$
$\therefore \frac{x_1}{x_2}=\frac{y_2}{y_1}$

Given,
$x_1=8\text{members}$
$y_1=10\text{days}$
$x_2=8-3=5\text{members}$
$y_2=\text{number of days}$

$\Rightarrow y_2=\frac{x_1\times y_1}{x_2}$

$\Rightarrow y_2=\frac{8\times 10}{5}=16\text{days}$