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

**Problem**

**Problem**

A and B invest $3000 and $4000 respectively in a business. If A doubles his capital after 6 months, in what proportion should one divide that year’s profit?

- 9 : 10
- 9 : 8
- 8 : 9
- 3 : 4
- 4 : 3

**The Usual Method**

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A’s investment = $3000 for 12 months and $3000 further for the 6 months.

i.e. 3000 x 12 + 3000 x 6 = 3000 x 18 = 54000

B’s investment = $4000 for 12 months

i.e. 4000 x 12 = 48000

Hence ratio of investments = 54000 : 48000 = 54 : 48 = 9 : 8 = ratio of profit

**(Ans: 2)**

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

**Using Technique**

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Since B’s investment remains constant at $4000 for 12 months, the proportion that B should get of the profit will be a multiple of 4. This eliminates all options other than ‘2’ and ‘4’. Also note that B’s total investment is less than that of A’s. Hence, A’s share of profit should be higher than B’s share. Thus option ‘4’ is also eliminated. Thus option ‘2’ is the answer.

**(Ans: 2)**

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

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