Q) The age of the father is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children. Find the present age of the father.

Ans: Let’s consider Father’ age be X and children’s age be Y and Z

Step 1: By first condition: father is twice the sum of the ages of his two children

∴ X = 2 (Y + Z)

∴ (Y + Z) = …….. (i)

Step 2: After 20 years, father’s age = (X + 20) and ages of children = (Y + 20) and (Z + 20)

By second condition: After 20 years, his age will be equal to the sum of the ages of his children

∴ X + 20 = (Y + 20) + (Z + 20)

∴ X + 20 = Y + Z + 40

∴ X = Y + Z + 20

∴ (Y + Z) = X – 20 ………. (ii)

By comparing equations (i) and (ii), we get:

= X – 20

∴ X = 2 (X – 20)

∴ X = 2 X – 40

∴ X = 40

Therefore, father’s present age is 40.

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