CAT 2022 Question Paper | Quant Slot 1

CAT Questions

CAT 2022 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 13 : 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

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Video Explanation

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Explanatory Answer

The ratio of the number of males to females is 5 : 4
The ratio of the number of literate males to literate females is 2 : 3.
The ratio of the number of illiterate males to illiterate females is 4 : 3.
Let,
The number of males to females is 5x, 4x
The number of literate males to literate females is 2y, 3y.
The number of illiterate males to illiterate females is 4z, 3z.

We know that the ratio of the number of males to females is 5 : 4
\( \frac { 2 y + 4 z } { 3 y + 3 z } = \frac { 5 } { 4 } \)
4(2y + 4z) = 5(3y + 3z)
8y + 16z = 15y + 15z
z = 7y

3600 males in the village are literate.
2y = 3600
y = 1800
Total number of females = 24y = 24(1800) = 43,200

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The answer is '43200'