Question

A farmer has enough food to feed his 18 cows for a week. If after 2 days, he bought 2 more cows, then how long will the food last?

• A. $4\frac{1}{2}days$
• B. $4days$
• C. $4\frac{2}{3}days$
• D. $5days$

Answer 1

The correct option is A $4\frac{1}{2}days$

Given, the food for 18 cows will last for 7 days.

After 2 days, 2 more cows were bought and number of days remaining is (7-2) = 5 days.

If the number of cows increase, then the number of days for which the food will last will decrease.

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

Given,
$x_1=18cows$
$y_1=5days$
$x_2=18+2=20cows$
$y_2=\text{Number of days for which}\text{the food will last for 20 cows}$

$\Rightarrow y_2=\frac{x_1\times y_1}{x_2}$
$\Rightarrow y_2=\frac{18\times 5}{20}=4\frac{2}{4}=4\frac{1}{2}days$

Hence, the food will last for 4 and a half days for 20 cows.