Question

10 years ago, the ratio of age of A and
B was 3 : 2 and after 10 vears, their
ages ratio will become 4 : 3. Find the
sum of their present age.
(1) 100
(2) 120
(3) 140
(4) 160
​

Answer 1

Answer:

120

Step-by-step explanation:

Their ages are 70 and 50

Answer 2

Answer:

Their present ages are in the ratio = x/y

Before 10 years their ages were in the ratio = 3/2 = x - 10/ y - 10 ( equation number 1 )

After 10 years their ages will be in the ratio = 4/2 = x + 10/ y + 10 ( equation number 2)

Simplifying both equations

1. x - 10/ y - 10 = 3/2

If we cross multiply we get

2x - 20 = 3y - 30 ..... 2x - 3y = -10

2. x + 10/ y + 10 = 4/3

If we cross multiply we get

3x + 30 = 4y + 40...... 3x - 4y = 10

Add both equations

2x - 3y = - 10

3x - 4y = 10

-4( 2x - 3y = - 10 ) = -8x + 12y = 40

3( 3x - 4y = 10 ) = 9x - 12y = 30

x = 70 years

2x - 3y = -10

2( 70 ) - 3y = - 10

140 - 3y = -10

-3y = -150

3y = 150

y = 50 years

x + y = 70 + 50

= 120 years