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Literate and Illiterate Population

CAT 2022 Slot 1 · Quantitative Ability · Medium · Ratio and Proportion

This is a medium Quantitative Ability question from the CAT 2022 Slot 1 paper. It tests Ratio and Proportion. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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In a village, the ratio of number of males to females is 5:45 : 4. The ratio of number of literate males to literate females is 2:32 : 3. The ratio of the number of illiterate males to illiterate females is 4:34 : 3. If 3600 males in the village are literate, then the total number of females in the village is

Answer

43200

Explanation

Literate males =3600= 3600. Since ratio of literate males to literate females is 2:32 : 3, Literate females =3600×32=5400= 3600 \times \frac{3}{2} = 5400.

Let number of illiterate males =4x= 4x and illiterate females =3x= 3x.

Total males =3600+4x= 3600 + 4x. Total females =5400+3x= 5400 + 3x.

We are given the ratio of total males to total females is 5:45 : 4: 3600+4x5400+3x=54\frac{3600 + 4x}{5400 + 3x} = \frac{5}{4} 4(3600+4x)=5(5400+3x)4(3600 + 4x) = 5(5400 + 3x) 14400+16x=27000+15x14400 + 16x = 27000 + 15x x=12600x = 12600

Total number of females =5400+3x=5400+3(12600)=5400+37800=43200= 5400 + 3x = 5400 + 3(12600) = 5400 + 37800 = 43200.

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