Question

Rajan is older than Samara by 5 years. Five years from now, the respective ratio between Rajan's age and Samara's age will be 7 ∶ 6. What was Rajan’s age 10 years ago? 

1. 20 years 
2. 25 years 
3. 22 years 
4. 23 years 
5. None of these

Answer 1

Correct Answer - Option 1 : 20 years 

Given

Rajan’s age = Samara’s age + 5

Ratio of their ages after 5 years = 7 ∶ 6

Formula used

Ratio formula, a ∶ b = a/b

Calculation

Let the age of Rajan = x

And let the age of Samara = y

According to question

⇒ x = y + 5

⇒ y = x – 5

After 5 years

⇒ (x + 5)/(y + 5) = 7/6

⇒ 6x + 30 = 7y + 35

⇒ 6x – 7y = 5

⇒ 6x – 7(x – 5) = 5

⇒ x = 30 years

Rajan’s age = 30 years

Rajan’s age 10 years ago = 30 – 10 = 20 years

∴ Rajan’s age after 10 years ago is 20 years.