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

**Problem**

**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?

- 35
- 40
- 18
- 15
- 12

**The Usual Method**

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

Hence, the number of gents = 2*x*

Thus,

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

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

**(Ans: 5)**

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

**Using Technique**

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Since, the original ratio of ladies to gents = 1 : 2, the total number of guests = 1*x* + 2*x* = 3*x*.

Also, the new ratio of ladies to gents = 1 : 3, the total number of guests = 1*y* + 3*y* = 4*y*

Hence the total number of guests should be a multiple of both 3 and should become a multiple of 4 after 4 is subtracted from it. This means that the original number of guest should be a multiple of 3 as well as 4 or a multiple of 12. The only option satisfying this condition is option ‘5’.

**(Ans: 5)**

*Estimated Time to arrive at the answer = 10 seconds.*

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