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# [Smart Math] Ratio Proportion Problem 21

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

### Problem

The ratio of the number of ladies to gents at a party was 1 : 2, but when 2 ladies and 2 gents leave, the ratio became 1 : 3. How many people were at the party originally?

1. 35
2. 40
3. 18
4. 15
5. 12

### The Usual Method

Let the original number of ladies in the party be ‘x’.

Hence, the number of gents = 2x

Thus, $\frac{x-2}{2x-2}=\frac{1}{3}$

$\therefore 3x-5=2x-2$

$\therefore x=4$

Hence, number of gents in the party = 2x = 8

Hence, total number of people in the party = 4 + 8 = 12.

(Ans: 5)

Estimated Time to arrive at the answer = 45 seconds.