Question

. in a forest different kinds of animals are there. In a particular place , Half of a herd of deer are grazing in the field and three fourths of the remaining are playing nearby. The rest 9 are drinking water from the pond. Then Q1- Find the total number of deer in the herd

Answer 1

$\large\underline{\sf{Solution-}}$

Let the total number of deer in the herd be x.

According to given question,

1. Half of a herd of deer are grazing in the field.

2. Three fourths of the remaining are playing nearby.

3. The rest 9 are drinking water from the pond.

Thus,

$\rm :\longmapsto\:\dfrac{x}{2} + \dfrac{3}{4}\bigg[x - \dfrac{x}{2} \bigg] + 9 = x$

$\rm :\longmapsto\:\dfrac{x}{2} + \dfrac{3}{4}\bigg[\dfrac{x}{2} \bigg] + 9 = x$

$\rm :\longmapsto\:\dfrac{x}{2} + \dfrac{3x}{8} + 9 = x$

$\rm :\longmapsto\:\dfrac{4x + 3x + 72}{8} = x$

$\rm :\longmapsto\:\dfrac{7x + 72}{8} = x$

$\rm :\longmapsto\:8x = 7x + 72$

$\rm :\longmapsto\:8x - 7x = 72$

$\bf\implies \:x \: = \: 72$

Verification :-

Total number of deer in herd = 72 deer

Half of a herd of deer are grazing in the field = 36 deer

Three fourths of the remaining are playing nearby = 3/4×36 = 27 deer

Rest drinking water from the pond = 72 - 36 - 27 = 9 deer

Hence, Verified