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CAT 2024 Slot 3 — QA Question 7

RatioEasy

Rajesh and Vimal own 20 hectares and 30 hectares of agricultural land, respectively, which are entirely covered by wheat and mustard crops. The cultivation area of wheat and mustard in the land owned by Vimal are in the ratio of 5 : 3. If the total cultivation area of wheat and mustard are in the ratio 11 : 9, then the ratio of cultivation area of wheat and mustard in the land owned by Rajesh is

Answer & solution

  • A

    1 : 1

  • B

    4 : 3

  • 7 : 9

  • D

    3 : 7

Solution

Medium

Compute Vimal's wheat and mustard from his 5:35:3 split, then use the overall 11:911:9 ratio across both farmers (total 5050 ha) to get the combined wheat and mustard. Subtract Vimal's share to recover Rajesh's.

1

Vimal's split. Vimal has 3030 ha in wheat : mustard =5:3=5:3 (8 parts).

Vimal wheat=58×30=18.75⇒ Vimal mustard=38×30=11.25\begin{aligned} &\text{Vimal wheat}=\frac{5}{8}\times 30=18.75\\ &\Rightarrow\ \text{Vimal mustard}=\frac{3}{8}\times 30=11.25 \end{aligned}
2

Combined split. Total land =20+30=50=20+30=50 ha, with total wheat : mustard =11:9=11:9 (20 parts).

Total wheat=1120×50=27.5⇒ Total mustard=920×50=22.5\begin{aligned} &\text{Total wheat}=\frac{11}{20}\times 50=27.5\\ &\Rightarrow\ \text{Total mustard}=\frac{9}{20}\times 50=22.5 \end{aligned}
3

Rajesh's share = total − Vimal.

Rajesh wheat=27.5−18.75=8.75[(2)-(1)]⇒ Rajesh mustard=22.5−11.25=11.25[(2)-(1)]⇒ ratio=8.7511.25=3545=79\begin{aligned} &\text{Rajesh wheat}=27.5-18.75=8.75\quad\text{[(2)-(1)]}\\ &\Rightarrow\ \text{Rajesh mustard}=22.5-11.25=11.25\quad\text{[(2)-(1)]}\\ &\Rightarrow\ \text{ratio}=\frac{8.75}{11.25}=\frac{35}{45}=\frac{7}{9} \end{aligned}
7:97:9
CAT 2024 Slot 3 QA Q7: Rajesh and Vimal own 20 hectares and 30 hectares of agricultural land, respectively, which are entirely covere — Solution | TheCATExam