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CAT 2022 Slot 1 — QA Question 2

RatioEasy

In a village, the ratio of number of males to females is 5 : 4. The ratio of number of literate males to literate females is 2 : 3. The ratio of the number of illiterate males to illiterate females is 4 : 3. If 3600 males in the village are literate, then the total number of females in the village is

Answer & solution

Answer: 43200

Solution

Easy

Use the literate-male count to get literate females directly. Let the illiterate counts share a variable, then force the overall male:female ratio 5:45:4 to fix that variable. Total females = literate females + illiterate females.

Ratios given: males : females =5:4=5:4; literate M : literate F =2:3=2:3; illiterate M : illiterate F =4:3=4:3; and literate males =3600=3600.

1

Find literate females from the 2:32:3 literacy ratio:

literate Mliterate F=23=3600literate F ⇒ literate F=5400\frac{\text{literate M}}{\text{literate F}}=\frac{2}{3}=\frac{3600}{\text{literate F}}\ \Rightarrow\ \text{literate F}=5400
2

Let illiterate males =4x=4x and illiterate females =3x=3x (their 4:34:3 ratio). Then total males =3600+4x=3600+4x and total females =5400+3x=5400+3x.

3

Impose the overall 5:45:4 ratio and solve for xx:

3600+4x5400+3x=544(3600+4x)=5(5400+3x)14400+16x=27000+15xx=12600\begin{aligned} &\frac{3600+4x}{5400+3x}=\frac{5}{4}\\ &4(3600+4x)=5(5400+3x)\\ &14400+16x=27000+15x\\ &x=12600 \end{aligned}
4

Total females:

5400+3x=5400+3(12600)=5400+37800=432005400+3x=5400+3(12600)=5400+37800=43200
43200\mathbf{43200}
CAT 2022 Slot 1 QA Q2: In a village, the ratio of number of males to females is 5 : 4. The ratio of number of literate males to liter — Solution | TheCATExam