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

**Problem**

**Problem**

The sum of present ages of A, B and C is 90 years. 6 years ago their sum were in the ratio 1 : 2 : 3. What is the present age of C?

- 24 years
- 30 years
- 32 years
- 42 years
- 60 years

**The Usual Method**

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Sum of present ages of A, B and C = 90 years. Hence sum of ages of A, B and C 6 years ago was = 90 – (6 x 3) = 72 years

This divided in the ratio of 1 : 2 : 3.

Hence age of C 6 years ago = 36 years.

Hence C’s present age = 36 + 6 = 42 years

**(Ans: 4)**

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

**Using Technique**

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As can be seen from the ratio of ages of A, B and C that C’s age was half of the total ages (C’s age = 3*x* out of 1*x* + 2*x* + 3*x* = 6*x*, hence half). Half of 90 is 45. Hence C’s age has to be close to 45, so 42 years.

(Note: The age of C will be less than 45 years, we applied the ratio 1 : 2 : 3 to 90 years instead of correctly applying it to 90 – 18 = 72 years)

**(Ans: 4)**

*Estimated Time to arrive at the answer = 5 seconds.*

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