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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?

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? Correct Answer Q<sub>1</sub> &lt; Q<sub>2</sub> &gt; Q<sub>3</sub>

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.

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