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

**Problem**

**Problem**

B invests $500 more than A in business, but A’s investment in the business is for 4 months, whereas B’s investment is for 3 months only. If A’s share of total profit of $520 is $40 more than B’s. How much did A contribute to business?

- $2500
- $3000
- $3500
- $4000
- $4500

**The Usual Method**

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Let earning by A = *a*

Hence, earnings by B = 520 – *a*

Also, *a* – (520 – *a*) = 40

Ratio of Earnings = Ratio of Investment

Hence, 280 : 240 or 7 : 6 = Ratio of Investment

Let the amount invested by A be $*x*

Hence, amount invested by B = $(*x* + 500)

Thus, ratio of investments by A and B is

**(Ans: 3)**

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

**Using Technique**

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First get the ratio of earnings of A and B by the usual method, i.e. 7 : 6.

The investment period of A is 4 months and 4 is not a factor of 7. The amount of investment has to be a factor of 7 so as to get 7 in the ratio. The only option which has a multiple of 7 is option ‘3’ $3500.

**(Ans: 3)**

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

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