Question

The ratio of number of men to number of women in a party is 5:4. If the number of men is 40, find the number of women in the party

Answer 1

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Since the ratio of women to men at the start was 3 : 2, the number of women was 3a and the number of men was 2a, for some a.

After 20 more men joined, the number of men became 2a+20.

As the ratio was then 2 : 3,

3 × (# women) = 2 × (# men)

=> 3 × 3a = 2 × (2a+20)

=> 9a = 4a + 40

=> 5a = 40

=> a = 8

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