Class A has boys to girls in the ratio 2 : 3, Class B has girls to boys in the…

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Class A has boys to girls in the ratio 2 : 3, Class B has girls to boys in the ratio 5 : 3. If the number of students in Class A is at least twice as many as the number of students in Class B, what is the minimum percentage of boys when both classes are considered together? 

  1. A.

    33.33%

  2. B.

    40%

  3. C.

    39.17%

  4. D.

    37.5%

Attempted by 147 students.

Show answer & explanation

Correct answer: C

Find the percentage of boys in each class.

  • Class A: boys to girls = 2:3, so boys = 2/(2+3) = 2/5 = 40%.

  • Class B: girls to boys = 5:3, so boys = 3/(5+3) = 3/8 = 37.5%.

To minimize the combined percentage of boys given that Class A has at least twice as many students as Class B, use the smallest allowed size for Class A: let Class A = 2k and Class B = k.

Compute total boys and total students:

  • Total boys = 2k × 40% + k × 37.5% = 2k×(2/5) + k×(3/8) = k×(4/5 + 3/8) = k×(32/40 + 15/40) = 47k/40.

  • Total students = 2k + k = 3k.

Fraction of boys = (47k/40) / (3k) = 47/120 ≈ 0.391666... which equals 39.166...%.

Therefore, the minimum percentage of boys when both classes are considered together is 39.17%.

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