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
Question:
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
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
Options
Answer: 43200
Explanation:
Let the total number of males = 5k and the total number of females = 4k. The ratio of literate males to literate females = 2 : 3. Given literate males = 3600 ⇒ Literate females = 3600 × (3 / 2) = 5400 Illiterate males = 5k - 3600 Illiterate females = 4k - 5400 Given ratio of illiterate males to illiterate females = 4 : 3 ⇒ (5k - 3600) / (4k - 5400) = 4 / 3 Cross multiplying: 3(5k - 3600) = 4(4k - 5400) 15k - 10800 = 16k - 21600 k = 10800 Total number of females = 4k = 4 × 10800 = 43200 Final Answer: 43200
Explanation:
Let the total number of males = 5k and the total number of females = 4k. The ratio of literate males to literate females = 2 : 3. Given literate males = 3600 ⇒ Literate females = 3600 × (3 / 2) = 5400 Illiterate males = 5k - 3600 Illiterate females = 4k - 5400 Given ratio of illiterate males to illiterate females = 4 : 3 ⇒ (5k - 3600) / (4k - 5400) = 4 / 3 Cross multiplying: 3(5k - 3600) = 4(4k - 5400) 15k - 10800 = 16k - 21600 k = 10800 Total number of females = 4k = 4 × 10800 = 43200 Final Answer: 43200
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