Question

Grass in lawn grown equally thick and in a uniform rate. It takes $24$ days for $70$ cows and $60$ days for $30$ cows to eat the whole of the grass. How many cows are needed to eat the grass in $96$ days?

• A. $20$ cows
• B. $24$ cows
• C. $28$ cows
• D. $32$ cows

Answer 1

The correct option is A $20$ cows

Let $n,g,r,$ and $c$ be the no. of cows, grass initially, the rate at which grass grow/day, and grass eaten by cow/day respectively.

Now according to the question-

It takes $24$ days for $70$ cows to eat the whole of the grass.

$g+24r=70\times 24c=1680c⟶\left(i\right)$

$g+60r=60\times 30c=1800c$

Again, given that it takes 60 days for 30 cows to eat the whole of the grass.

$\therefore g=1800c-60r⟶\left(ii\right)$

From ${eq}^n\left(i\right)\&\left(ii\right)$, we have

$c=\frac{3}{10}r⟶\left(iii\right)$

Now, to eat the grass in 96 days-

$g+96r=96\times nc$

$\Rightarrow 96\times nc=1800c-60r+96r=1800c+36r=1800c+120c=1920c$

$\Rightarrow n=20$

Hence, $20$ cows are needed to eat the grass in $96$ days.