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      Question

      In College A, the ratio of boys to girls is 3:2, while

      in College B, the ratio is 7:3. If 20% of the boys from College A are undergraduates and 60% of the girls from College B are postgraduates, the postgraduate boys from College A and postgraduate girls from College B combined amount to 3300 students. Assuming the total number of students is equal in both colleges, determine the total male Students in College A and the female Students in College B. 
      A 6598 and 1500 Correct Answer Incorrect Answer
      B 3500 and 2000 Correct Answer Incorrect Answer
      C 3500 and 1500 Correct Answer Incorrect Answer
      D 2500 and 1000 Correct Answer Incorrect Answer
      E none of these Correct Answer Incorrect Answer

      Solution

      Given: Number of boys in College A = 3x Number of girls in College A = 2x Number of boys in College B = 7y Number of girls in College B = 3y Total students are equal: 3x+2x=7y+3y So, 5x=10y or x=2y. Postgraduate Students: Number of postgraduate boys in College A = 80% of 3x = 0.8×3x=2.4x Number of postgraduate girls in College B = 60% of 3y = 0.6×3y=1.8y Since x=2y: 2.4(2y)+1.8y=3300 4.8y+1.8y=3300 6.6y=3300 y=500 Therefore, x=2y=2×500=1000. Hence, Total male students in College A:3x=3×1000=3000 Total female students in College B:3y=3×500=1500

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