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
- 5 : 4
- 2 : 1
- 4 : 3
- 3 : 2
The Correct Option is A
Solution and Explanation
Let the current age of Rajesh be R, and the current age of Garima be G. According to the problem, when Rajesh's age was the same as the present age of Garima, the age ratio was 3:2.
Suppose it was x years ago that Rajesh's age was equal to Garima's current age. Therefore, at that time, Rajesh's age was R - x = G, and Garima's age was G - x.
We have the ratio:
\( \frac{R-x}{G-x} = \frac{3}{2} \)
Cross-multiplying gives:
\(2(R-x) = 3(G-x)\)
Expanding and simplifying:
\(2R - 2x = 3G - 3x\)
\(2R + x = 3G\) … (Equation 1)
Now, suppose after y years, Garima's age becomes equal to Rajesh's present age R. Then Garima's age will be G + y = R, and Rajesh's age will be R + y.
The future age ratio is given as 5:4:
\( \frac{R+y}{R} = \frac{5}{4} \)
Cross-multiplying gives:
\(4(R+y) = 5R\)
Expanding and simplifying:
\(4R + 4y = 5R\)
\(4y = R\) … (Equation 2)
Substituting from Equation 2 into Equation 1, where y=R/4:
\(2R + (R/4) = 3G\)
\(8R + R = 12G\)
\(9R/4 = 3G\)
\(3R = 4G\)
Now, solving gives the ratio of future age of Rajesh to Garima:
\(\frac{R+R/4}{R} = \frac{5}{4}\)
Thus, the ratio of Rajesh's future age to Garima's current age as their future age becomes equal to Rajesh's current age is indeed:
5:4
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