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[Smart Math] Ratio Proportion Problem 28

Here’s and example of a SMART MATH problem for RATIO PROPORTION. Problem

The ratio of number of ladies to gents in a party was 3 : 2. When however, 20 more gentlemen joined the party, the ratio was reversed. How many ladies were there at the party?

1. 16
2. 24
3. 32
4. 36
5. 40

The Usual Method

Let ‘x’ be the constant of proportionality. Hence, there will be 3x ladies and 2x gents in the party originally.

New total number of gents = 2x + 20

Hence, ratio of ladies to gents = $\frac{3x}{2x+20}=\frac{2}{3}$ $\therefore 9x=4x+40$ $\therefore 5x=40$ $\therefore x=8$ $\therefore$Original number of ladies = 3x = 3 x 8 = 24

(Ans: 2)

Estimated Time to arrive at the answer = 45 seconds.

Using Technique

Since the total number of ladies at the party = 3x, the answer should be a multiple of 3. From the options, only option ‘2’ and ‘4’ are multiples of 3. Assuming option ‘2’ to be the right answer, the number of men becomes 2x = 16 (using 3x = 24 $\therefore x=8$) Hence, new total of gents = 20 + 16 = 36 and 24 : 36 = 2 : 3. This satisfies the conditions and so, ‘2’ is the right option.