simple equations STD VI

Half of a herd of deer are grazing in the field and three fourths of the remaining is playing nearby. The rest 9 are drinking water from the pond. Find the number of deer in the herd.

Answer:

Let the number of deer be y

No. of deer grazing = y/2

Remaining no. of deer = 1-y/2 = y/2

No. of deer playing = ¾ x y/2 = 3y/8

Given that, y – (y/2 + 3y/8) = 9

Or, y – y(4+3)/8 = 9

Or, y(1 – 7/8) = 9

Or, y x 1/8 = 9

Or, y = 72.

A grandfather is ten times older than his granddaughter. He is also 54 years older than her. Find their present ages.

Answer:

Let the age of the granddaughter be y

So, the age of the grandfather is 10y.

Also given that 10y – y = 54

Or, 9y = 54

Or, y = 6 years

So, the age of the granddaughter is 6, and the age of the grandfather is 60.

Aman’s age is three times his son’s age. Ten years ago he was five times his son’s age. Find their present ages.

Answer:

Let son’s age by y

So, Aman’s age is 3y

Also given that, 5 x (y-10) = 3y – 10

Or, 5y – 50 = 3y – 10

Or, 5y – 3y = 50 – 10

Or, 2y = 40

Or, y = 40/2 = 20

So, the son’s age is 20 years and Aman’s age is 60 years.