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 :

• A. 5:4
• B. 4:5
• C. 2:3
• D. 4:3
• E. 7:6

Hint:

Use the time difference concept: the same number of years ago or hence applies to both ages. Let the difference between their ages be constant.

Answer 1

The Correct Option is D

Step 1: Let present ages: Rajesh = $R$, Garima = $G$.
Step 2: When Rajesh's age was same as Garima's present age, that was $R - G$ years ago. At that time: Rajesh's age = $G$, Garima's age = $G - (R - (g) = 2G - R$. Given ratio: $\frac{G}{2G - R} = \frac{3}{2} \implies 2G = 6G - 3R \implies 3R = 4G \implies R = \frac{4G}{3}$.
Step 3: When Garima's age becomes same as Rajesh's present age, that will be $R - G$ years from now. At that time: Rajesh's age = $R + (R - (g) = 2R - G$, Garima's age = $R$. Ratio = $\frac{2R - G}{R}$.
Step 4: Substitute $R = \frac{4G}{3}$: $2R - G = 2 \times \frac{4G}{3} - G = \frac{8G}{3} - \frac{3G}{3} = \frac{5G}{3}$. Ratio = $\frac{5G/3}{4G/3} = \frac{5}{4}$? Wait, careful: $\frac{2R - G}{R} = \frac{5G/3}{4G/3} = \frac{5}{4}$.
Step 5: That gives ratio 5:4. But the question asks for ratio of ages of Rajesh and Garima at that time, which is $(2R - (g) : R = 5 : 4$. However, the optionss include 4:3, 5:4, etc. Let's check again. When Garima's age becomes $R$, Rajesh's age becomes $R + (R - (g) = 2R - G$. So ratio Rajesh : Garima = $(2R - (g) : R$. From $3R = 4G$, $G = \frac{3R}{4}$. Then $2R - G = 2R - \frac{3R}{4} = \frac{8R - 3R}{4} = \frac{5R}{4}$. So ratio = $\frac{5R}{4} : R = 5 : 4$.
Step 6: Thus the ratio is 5:4. But the answer given in the extraction is 4:3? Let's verify the interpretation: "When Garima's age becomes the same as the present age of Rajesh" means Garima's age = $R$. The ratio of ages of Rajesh and Garima will be Rajesh : Garima = $(2R - (g) : R = 5:4$.
Step 7: Final Answer: 5:4.