Q) Five years hence, fathers age will be three times the age of son. Five years ago, father was seven times as old as his son. Find their present ages.

Q31 C – Sample Question Paper – Set 1 – Maths Standard – CBSE 2026

Ans: Let’s consider the father’s age is X and son’s age is Y.

Step 1: By 1st condition: “Five years hence, fathers age will be three times the age of son.”

∴ (X + 5) = 3 (Y + 5)

∴ X + 5 = 3 Y + 15

∴ X – 3 Y = 15 – 5

∴ X – 3 Y = 10 …………………. (i)

Step 2: 

By 2nd condition: “Five years ago, father was seven times as old as his son.”

∴ (X – 5) = 7 (Y – 5)

∴ X – 5 = 7 Y – 35

∴ X – 7 Y = – 35 + 5

∴ X – 7 Y = – 30 …………(ii)

Step 3: By deducting equation (ii) from equation (i), we get:

(X – 3 Y) – (X – 7 Y) = 10 – (- 30)

∴ X – 3 Y – X + 7 Y = 10 + 30

∴ 4 Y = 40

∴ Y = 40 / 4

∴ Y = 10 years

Step 4: By substituting value of Y in equation (i), we get:

∵ X – 3 Y = 10

∴ X – 3 (10) = 10

∴ X = 10 + 30

∴ X = 40 years

Therefore, the father’s present age is 40 years and son’s present age is 10 years.

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