CAT 2022 Slot 1 QA Q13 Ratio, Mixtures & Averages

Question 13 of the Quantitative Ability (QA) section, CAT 2022 Slot 1, with CAT's official answer and a worked solution.

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

TITA: type in the answer. There are no options and no negative marking.

Answer: 43200 Ratio, Mixtures & Averages TITA

Solution

  1. Males \(= 5k\), females \(= 4k\). Literate males \(= 3600\), so literate females \(= \frac{3}{2} \times 3600 = 5400\).
  2. Illiterates: males \(5k - 3600\), females \(4k - 5400\), with \(\frac{5k - 3600}{4k - 5400} = \frac43\).
  3. \(15k - 10800 = 16k - 21600 \Rightarrow k = 10800\).
  4. Females \(= 4k = 43200\).

Same concept in other years

More Ratio, Mixtures & Averages questions from CAT

All 84 Ratio, Mixtures & Averages questions asked since 2017.