Question

5 years ago, sisters age was 5 times the age of her brother and the sum of present ages of sister and brother is 34 years what will be the age of her brother after 6 year?

Answer 1

let present age of sister = x

let present age of brother = y

x + y = 34             [ given sum of present age = 34]

x = 34 - y      ---------------------- eq 1

FIVE YEARS AGO

Age of Sister = x -5

Age of brother = y - 5

Given that (x - 5) = 5 × ( y - 5)

⇒ x - 5 = 5y - 25

⇒ x - 5y = - 20      -----------------------------eq 2

substituting value of x from eq1 in eq 2

(34 - y) - 5y = -20

⇒ 34 - 6y = -20

⇒ -6y = -54

⇒ y = 9

So Age of brother after 6 year = y + 6 = 9 + 6 = 15 years

Answer 2

Let x and y be the present age of sister and brother.
x + y = 34.........(1)
x - 5 =5( y - 5)
x - 5 =5y - 25
x -5y= -20........(2)
Substracting eqn. (1) & (2), we get
-6y = -54
y = 9
Therefore, age of brother is 9.
After 6 years = y + 6
=9 + 6
= 15