In class A, the ratio of boys to girls is 2 : 3. In class B the ratio of boys…

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In class A, the ratio of boys to girls is 2 : 3. In class B the ratio of boys to girls is 4 : 5. If the ratio of boys to girls in both classes put together is 3 : 4, what is the ratio of number of girls in class A to number of girls in class B?

  1. A.

    3/5

  2. B.

    2/5

  3. C.

    3/4

  4. D.

    1/2

Attempted by 17 students.

Show answer & explanation

Correct answer: A

Let class A have 2x boys and 3x girls, and class B have 4y boys and 5y girls.

Total boys = 2x + 4y. Total girls = 3x + 5y. The combined boys:girls ratio is given as 3:4, so

(2x + 4y) / (3x + 5y) = 3 / 4.

  • Multiply both sides: 4(2x + 4y) = 3(3x + 5y) ⇒ 8x + 16y = 9x + 15y.

  • Rearrange: 16y − 15y = 9x − 8x ⇒ y = x.

Since x = y, the number of girls in class A to class B is 3x : 5y = 3x : 5x = 3 : 5. Answer: 3:5

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