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

**Problem**

**Problem**

A, B and C invest $5000, $4000 and $6000 respectively in a business. B gets 25% of the profit for managing the business and the remaining profit is divided amongst A, B and C in the proportion of their investments. If B gets $100 less than A and C together, what is the profit?

- $1500
- $750
- $500
- $1000
- $2500

**The Usual Method**

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Ratio of investments of A, B and C = 5 : 4 : 6. Let the profit be $‘*x*’.

Hence profit to be divided = *x* – 0.25*x* = 0.75*x*

Hence share of A =

Similarly, share of B =

And share of C =

Now since share of B = $100 less than A and C together,

$1000

**(Ans: 4)**

*Estimated Time to arrive at the answer = 75 seconds.*

**Using Technique**

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Note that the ratio of investments of A, B and C is 5 : 4 : 6. Hence they will get a total of 5*x* + 4*x* + 6*x* = 15*x*.

Now observe the options. Since B initially gets 25% of the profit, the remaining 75% is to be divided amongst A, B and C. This remaining 75% of the profit should be divisible by 15. (from 15*x*), so that the shares of A, B and C are whole numbers.

So for option ‘4’ => 1000 = 250 (25%) + 750 (75%).

Here the 75% i.e $750 is divisible by 15 and hence it is the answer.

(Note: We hit upon option ‘4’ straight as it is the easiest to break in 25% and 75%)

**(Ans: 4)**

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

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