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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

CAT · 2024 · Quant Slot 2
Question:
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

Options

4 : 3
2 : 1
3 : 2
5 : 4
Answer: 5 : 4

Explanation:
Let the difference in their ages = R − G At that time, Rajesh’s age = G, Garima’s age = G − (R − G) = 2G − R Given ratio: Rajesh : Garima = 3 : 2 ⇒ G : (2G − R) = 3 : 2 Solve for R in terms of G: 2G : (2 × (2G − R))? Wait step carefully: Ratio equation: G / (2G − R) = 3 / 2 ⇒ 2 × G = 3 × (2G − R) ⇒ 2G = 6G − 3R ⇒ 3R = 6G − 2G = 4G ⇒ R = 4G / 3 Future ratio when Garima reaches R (present age of Rajesh): Time passed = R − G = 4G/3 − G = G/3 Future ages: Rajesh = R + G/3 = 4G/3 + G/3 = 5G/3 Garima = G + G/3 = 4G/3 Ratio = Rajesh : Garima = (5G/3) : (4G/3) = 5 : 4

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