IPMAT Indore 2025 · Quantitative Ability · Question 1
IPMAT Indore 2025 previous year question on Linear Equations, with the answer and a step-by-step solution.
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 ____
Answer & solution
Answer: 36
Step 1 — father’s present age. Monica is one-third of her father’s age, so
\text{Father}=3\times 18=54\text{years}
Step 2 — let t years pass. After t years Monica is 18+t and her father is 54+t. We want Monica to be half her father’s age:
18+t=\frac{54+t}{2}
Step 3 — solve.
36+2t=54+t \Rightarrow t=18
Step 4 — answer what was asked. The question asks for Monica’s age, not the number of years:
18+18=36
Quick check: father is then 54+18=72, and 36 is indeed half of 72. ✓
Answer: 36
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