Question

Six years ago, Natasha's age was triple the age of Manasa. Six years later, Natasha's age will be 5/3 of the age of Manasa. What is the present age of Manasa?
1. 12
2. 11
3. 13
4. 14

Answer 1

Correct Answer - Option 1 : 12

Given: 

Six years ago, Natasha's age was triple the age of Manasa and Six years later, Natasha's age will be 5/3 of the age of Manasa

Calculation: 

Let the present age of Natasha is X years and Manasa is Y years

According to the question

Six years ago,

⇒ (X - 6) = 3 × (Y - 6)

⇒ X - 6 = 3Y - 18

⇒ X - 3Y = -12     . . .  (1)

Now,

Six years later

⇒ (X + 6) = 5/3(Y + 6)

⇒ 3X + 18 = 5Y + 30

⇒ 3X - 5Y = 12    . . .  (2)

In the first equation multiplied by 3, then subtracted from equation (2)

⇒ 3X - 5Y - 3X + 9Y = 12 + 36

⇒ 4Y = 48

⇒ Y = 48/4

⇒ Y = 12

∴ The present age of Manasa is 12 years.