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The present ratio of the ages of Tom and his father is 6 ∶ 10. 8 years ago, the ratio of ages of Tom and his father was 5 ∶ 9. What is the present age of Tom's father?

The present ratio of the ages of Tom and his father is 6 ∶ 10. 8 years ago, the ratio of ages of Tom and his father was 5 ∶ 9. What is the present age of Tom's father? Correct Answer 80

Given:

Present ratio of ages = 6 ∶ 10

The ratio of ages 8 years ago = 5 ∶ 9

Calculation:

Let the present age of Tom and his father be T and F respectively

The present ratio of ages

⇒ T/F = 6/10

⇒ 5T = 3F

⇒ T = 3F/5      ---(i)

The ratio of ages (8 years ago)

⇒ (T - 8)/(F - 8) = 5/9

⇒ 9T - 72 = 5F - 40

Substituting the value of T from equation (i)

⇒ 9 × (3F/5) = 5F + 32

⇒ 27F = 25F + 160

⇒ 2F = 160

⇒ F = 80

∴ The present age of Tom's father is 80 years

Shortcut Trick

Present age of Tom's father = Multiple of 10

Option 1 is not a multiple of 10 thus can be eliminated

Present age of Tom's father - 8 = Multiple of 9

Checking remaining options,

(2) 60 - 8 = 52 (Not a multiple of 9)

(3) 70 - 8 = 62 (Not a multiple of 9)

(4) 80 - 8 = 72 (Multiple of 9)

∵ Only the fourth options satisfy the condition 

∴ The present age of Tom's father is 80 years

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