Question

One third of the herds of cows are grazing in the field, $20$ less, than half of them are near the river. The remaining $35$ are tied with the trees. Find the total number of cows in the herd.

Answer 1

Suppose total cows $=x$

then grazing $=\frac{x}{3}$

near river $=\frac{x}{2}-20$

remaining $=35$

So grazing + river +remainder $=x$

So $\frac{x}{3}+\frac{x}{2}-20+35=x$

$\frac{2x+3x}{6}+15=x\Rightarrow 15=x-\frac{5x}{6}=\frac{x}{6}$

$\Rightarrow x=90$ i.e $x=15\times 6=90$