Correct Answer - Option 4 : 7 : 3
Given:
The ratio of father and son 5 years ago = 5 ∶ 3
Calculation:
Let the age of father and son, 5 years ago be 5x and 3x respectively
Then, Present age of Father = 5x + 5
The present age of son = 3x + 5
After 10 years,
The age of father = 5x + 5 + 10 = 5x + 15
The age of son = 3x + 5 + 10 = 3x + 15
Ratio of father and son = (5x + 15)/(3x + 15)
Checking the given option one by one
Option 1,
(5x + 15)/(3x + 15) = 3/2
⇒ 10x + 30 = 9x + 45
⇒ x = 15
It gives positive value so it can be the ratio of their age
Option 2,
(5x + 15)/(3x + 15) = 8/7
⇒ 35x + 105 = 24x + 120
⇒ x = 15/11
It gives positive value so it can be the ratio of their age
Option 3,
(5x + 15)/(3x + 15) = 6/5
⇒ 25x + 75 = 18x + 90
⇒ x = 15/7
It gives positive value so it can be the ratio of their age
Option 4,
(5x + 15)/(3x + 15) = 7/3
⇒ 15x + 45 = 21x + 105
⇒ x = -60/6 = -10
Age can not be in negative
∴ 7 ∶ 3 can not be the ratio of their ages after 10 years
