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CAT 2024 Slot 2 — QA Question 11

RatioEasy

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

Answer & solution

  • 5 : 4

  • B

    4 : 3

  • C

    2 : 1

  • D

    3 : 2

Solution

Medium

The age difference between two people is constant. Use that fixed difference to translate each "when ages match" statement, find the present ratio R:GR:G, then shift forward to the asked moment.

1

Use the first condition. Let present ages be RR (Rajesh) and GG (Garima). "When Rajesh's age was GG" was R−GR-G years ago; then Garima's age was G−(R−G)=2G−RG-(R-G)=2G-R, and the ratio was 3:23:2.

G2G−R=32⇒ 2G=3(2G−R)(cross-multiply)⇒ 2G=6G−3R ⇒ 3R=4G ⇒ RG=43\begin{aligned} &\frac{G}{2G-R}=\frac32\\ &\Rightarrow\ 2G=3(2G-R) \quad\text{(cross-multiply)}\\ &\Rightarrow\ 2G=6G-3R\ \Rightarrow\ 3R=4G\ \Rightarrow\ \frac{R}{G}=\frac43 \end{aligned}
2

Move to the future moment. Take R=4, G=3R=4,\,G=3 (difference =1=1). "When Garima's age becomes RR" is R−G=1R-G=1 year ahead; then Rajesh is R+1R+1 and Garima is G+1=RG+1=R.

Rajesh=2R−G=2(4)−3=5Garima=R=4\begin{aligned} &\text{Rajesh}=2R-G=2(4)-3=5\\ &\text{Garima}=R=4 \end{aligned}
3

Form the future ratio.

Rajesh:Garima=5:4\begin{aligned} &\text{Rajesh}:\text{Garima}=5:4 \end{aligned}
5:45:4
CAT 2024 Slot 2 QA Q11: When Rajesh's age was same as the present age of Garima, the ratio of their ages was 3 : 2. When Garima's age — Solution | TheCATExam