Question

Question 1 The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differs by 30 years. Find the ages of Ani and Biju.

Class 10 - Math - Pair of Linear Equations in Two Variables Page 68

Answer 1

Let the ages of Ani & Biju be x years & y yr.

A.T.Q

x- y = +-3 .................(i)
[ We don't know whether x>y or y>x]

Also age of Ani's fathers Dharam= 2x yr

Age of Biju's sister= y/2 yr

A.T Q

2x- y/2 = 30

4x - y = 60...................(ii)

Case 1: when x-y =3..............(iii)

On subtracting equation iii from equation ii

(4x- x) - y+ y= 60-3

3x= 57
x=57/3= 19

x= 19

On putting X= 19 in equation iii we get

x-y = 3
19-y= 3
19-3= y
y= 16

Case 2:
When x-y = 3..............(IV)

On subtracting equation IV from equation ii we get

4x-x -y + y= 60+3
3x= 63
x= 63/3
X= 21

On putting x = 21 in equation iv
x- y= -3
21-y = -3
-y -3-21
-y= -24

y= 24

Hence, age of Ani is 19 years and age of Biju is 16 years or age of Ani is 21 year & age of Biju is 24 year.

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Hope this will help you......