IPMAT Indore 2025 (SA) - Monica, who is 18 years old, is one-third the age of her father. The age at which she will be half the age of her father is ____ | PYQs + Solutions | AfterBoards
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IPMAT Indore 2025

Algebra
>
Linear Equation

Easy

Monica, who is 18 years old, is one-third the age of her father. The age at which she will be half the age of her father is ____

Entered answer:

✅ Correct Answer: 36
Monica is 18 years old and her age is one-third of her father's age.
Let's find the father's current age:
18=F318 = \dfrac{F}{3}
F=18×3=54F = 18 \times 3 = 54
So Monica's father is 54 years old.
After xx years, Monica will be half her father's age.
After xx years: \newline - Monica's age: 18+x18 + x \newline - Father's age: 54+x54 + x
According to the question:
(18+x)=(54+x)2(18 + x) = \dfrac{(54 + x)}{2}
36+2x=54+x36 + 2x = 54 + x
36+2x−54−x=036 + 2x - 54 - x = 0
x−18=0x - 18 = 0
x=18x = 18
Monica's age at that time will be 18+18=3618 + 18 = 36 years old.
When Monica is 3636, her father will be 7272 (double the age), confirming our answer.
The age at which Monica will be half the age of her father is 3636.

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