Question

Half of the herd of deer are grazing in the field and three fourths of the remaining are playing nearby. If the remaining 9 are drinking water from a pond , then the difference between the number of deer who are grazing and those who are playing is multiple of
A) 4
B) 6
C) 8
D) 9

Answer 1

Hint: From the question , we can see that the total deers are split into three types that are grazing in the field , which are playing nearby , which are drinking water from a pond. We know the fraction of the deers which are grazing and playing nearby , and we know that the number of deers drinking water is 9. Add all these by taking the total herd number as some variable.

Complete step by step answer:
Let us assume that the strength of the herd is A.
It is given that half of the herd of deer are grazing in the field , three fourth of the remaining herd of deer are playing nearby and the remaining 9 are drinking water from the pond.
Which implies the number of deers which are grazing = $\dfrac{1}{2}A = \dfrac{A}{2}$
and also , The number of deers which are playing nearby
  = three fourth of the remaining herd = $\dfrac{3}{4}$ (A- $\dfrac{A}{2}$) = (3A/8)
Given that the remaining deers that are drinking from the pond are 9
We know that when we add the no. of deers that are grazing in the field and that are playing nearby and that are drinking in the pond it should be the total herd strength as there is nothing left out.
Which implies A = (A/2) + (3A/8) + 9
=> (A/8) = 9
=> A = 72
We know that A is the strength of the total herd.
=> the number of deers which are grazing = (A/2) = 36
and the number of deers which are playing nearby = (3A/8) = 27
So the difference will be 36-27 = 9
We know that every number is a multiple of itself , so 9 is the multiple of 9.

So, the correct answer is “Option D”.

Note: Read the question carefully. It is given that three fourths of the ‘remaining’ deers are playing nearby. Many students make a wrong assumption that it is three fourth of the total herd which can change the answer in many cases. Do not make calculation mistakes.