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

**Problem**

**Problem**

A certain sum of money is divided between A, B and C in the proportion of 2 : 3 : 4. If C were to give B $20, and B were to give A half of what he has now, the amounts which A and C have now would be same. What is the amount divided between the three?

- $420
- $480
- $500
- $540
- $600

**The Usual Method**

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Let the shares of A, B and C be 2*x*, 3*x* and 4*x* respectively. (where ‘*x*’ is the constant of proportionality)

Thus,

(4*x* – 20) is the new share of C

is the new share of B and

2*x* + is the new share of A.

Also, since new shares of A and C are equal:

2*x* + = (4*x* – 20)

Hence total sum = $540

**(Ans: 4)**

*Estimated Time to arrive at the answer = 60 seconds.*

**Using Technique**

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Total sum of money to be shared = . Hence the sum should be a multiple of 9. Only option ‘4’ ($540) is a multiple of 9. This eliminates all the other options, so option ‘4’ is the answer.

**(Ans: 4)**

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

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