ThinkCAT Logo
ThinkCAT
Sign up
QuestionsMocksResourcesAnalytics

CAT 2024 Slot 2 QA Question 17

Multiple choice (+3 / −1) · Arithmetic · Ratio, Proportion & Variation · Try it, then check the answer and solution below.

CAT 2024 Slot 2QAArithmetic • Ratio, Proportion & VariationModerate
When Rajesh's age was same as the present age of Garima, the ratio of their ages was 3:
2
When Garima's age becomes the same as the present age of Rajesh, the ratio of the ages of Rajesh and Garima will become
Practice More Questions
Answer and solution

Answer: B) 5:4

📌 Core Concept
The problem involves age ratios and requires setting up equations based on given conditions. The key is to recognize that the difference in ages remains constant over time.
🔢 Step-by-Step Solution
1
Define Variables:
Let Rajesh's current age = R$
Let Garima's current age = G$
2
First Condition:
When Rajesh was GG years old, Garima's age was 2G−R2G - R.
The ratio was 3:23:2:
G2G−R=32\frac{G}{2G - R} = \frac{3}{2}
Solving:
2G=3(2G−R)  ⟹  2G=6G−3R  ⟹  3R=4G  ⟹  R=43G2G = 3(2G - R) \implies 2G = 6G - 3R \implies 3R = 4G \implies R = \frac{4}{3}G
3
Second Condition:
When Garima's age becomes R,thetimeelapsedisR , the time elapsed isR - G$.
Rajesh's age then will be R+(R−G)=2R−GR + (R - G) = 2R - G.
Substitute R=43GR = \frac{4}{3}G:
2R−G=2(43G)−G=83G−G=53G2R - G = 2\left(\frac{4}{3}G\right) - G = \frac{8}{3}G - G = \frac{5}{3}G
Garima's age then is R=43GR = \frac{4}{3}G.
Ratio:
53G43G=54\frac{\frac{5}{3}G}{\frac{4}{3}G} = \frac{5}{4}
⚡ 30-Second Shortcut
Recognize the constant age difference

Keep going

Related Ratio, Proportion & Variation questions