Question

Five years ago, the ratio of the ages of a father and his son was 5 : 3. Which of the following cannot be the ratio of their ages 10 years from now?

• A. 3 : 2
• B. 8 : 7
• C. 6 : 5
• D. 7 : 3

Answer 1

Answer:

D. 7 : 3

Solution: 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