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

**Problem**

**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?

- 16
- 24
- 32
- 36
- 40

**The Usual Method**

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

New total number of gents = 2*x* + 20

Hence, ratio of ladies to gents =

Original number of ladies = 3*x* = 3 x 8 = 24

**(Ans: 2)**

*Estimated Time to arrive at the answer = 45 seconds.*

**Using Technique**

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Since the total number of ladies at the party = 3*x*, 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 2*x* = 16 (using 3x = 24 ) Hence, new total of gents = 20 + 16 = 36 and 24 : 36 = 2 : 3. This satisfies the conditions and so, ‘2’ is the right option.

**(Ans: 2)**

*Estimated Time to arrive at the answer = 15 seconds.*

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