1.

Six years ago, the ratio of the ages of Ramesh and Sundar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is the present age of Sundar?1. 16 years2. 20 years3. 18 years4. None of the above

Answer» Correct Answer - Option 1 : 16 years

Given

Six years ago, the ratio of the ages of Ramesh and Sundar was 6 : 5

Four years hence, the ratio of their ages will be 11 : 10

Calculation

Let present age of Ramesh is x years and

Present age of Sundar is y years 

Now,

Six year ago age of Ramesh and Sundar 

⇒ Ramesh age six year ago = (x - 6) years

⇒ Sundar age six year ago = (y - 6) years

From question 

⇒ (x - 6) ∶ (y - 6) = 6 ∶ 5

⇒ (x - 6)/(y - 6) = (6/5)

⇒ 5x - 30 = 6y - 36

⇒ 6y - 5x = 6    ....(1)

Now, four years hence

⇒ Ramesh age four years hence = (x + 4)

⇒ Sundar age four years hence = (y + 4)

From question 

⇒ (x + 4) ∶ (y + 4) =11 ∶ 10

⇒ (x + 4)/(y + 4) = 11/10

⇒ 10x + 40 = 11y + 44

⇒ 10x - 11y = 4    ....(2)

Multiply equation (1) on both side by 2 

⇒ (6y - 5x = 6) × 2

⇒ 12y - 10x = 12    ....(3)

Now add equation (2) and equation (3)

⇒ 10x - 11y + 12y - 10x = 12 + 4

⇒ y = 16

⇒ Sundar present age = 16 years

∴ Sundar present age = 16 years


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