Question

Five years ago the average of the ages of P and Q was 40 years and now the average of the ages of Q and R is 48 years.

Q₁ : What is the present age of P if the sum of age of P and R is 70?

Q₂ : What is the present age of Q if the present age of P is 20% less than the present age of R?

Q₃ : What is the present age of R if the average age of P and R is 45 years?

Which option represent correct relation among Q₁, Q₂, and Q₃?

1. Q₁ < Q₂ < Q₃
2. Q₁ > Q₂ > Q₃
3. Q₁ < Q₂ > Q₃
4. Q₁ = Q₂ < Q3
5. Q₁ < Q₂ = Q₃

Answer 1

Correct Answer - Option 3 : Q₁ < Q₂ > Q₃

Calculation:

⇒ Sum of present age of P and Q = P + Q = 90      ----(1)

⇒ Sum of present age of Q and R = Q + R = 96     ----(2)

⇒ For Q₁ Sum of P and R 

⇒ P + R = 70     ----(3)

⇒ By solving Eq. (1), (2), and (3)

⇒ Q₁ = Present age of P = 32 years

⇒ For Q₂ present age P, 20% less than the present age of R.

⇒ P = 4R/5     ----(4)

⇒ By solving Eq. (1), (2), and (4)

⇒ Q₂ = Present age of Q = 66 years.

⇒ For Q₃, the average age of P and R is 45

⇒ P + R = 45 × 2,

⇒ P + R = 90     ----(5)

⇒ By solving Eq. (1), (2), and (5)

⇒ Q₃ = present age of R = 48 years.

∴ The required result will be Q1 < Q2 > Q₃.