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

**Problem**

**Problem**

B receives 1/8^{th} of the profit of business as wages and the rest is divided between B and A in proportion to their capitals of $6000 and $8000 respectively. If in 1 year, B receives $1000 totally, what does A receive?

- $800
- $1000
- $1200
- $1250
- $1500

**The Usual Method**

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Assuming the total profit = ‘*p*’

Hence, 1/8^{th} of profit =

Balance profit =

This balance profit is divided in the ratio of investments i.e. 6000 : 8000 = 3 : 4

Hence total earnings of A =

Similarly, total earnings of B = = $1000

*p* = $2000

Hence, A’s share = = $1000

**(Ans: 2)**

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

**Using Technique**

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Visualize that the total profit is divided in 8 parts, of which 1 part goes to B as wages and the remaining 7 parts are divided between B and A in the ratio of 6000 : 8000 or 3 : 4. Thus B receives 3 more parts of the profit and A receives 4 parts. Thus B receives in total 3 + 1 = 4 parts of the profit which is same as 4 parts received by A. Thus A receives the same money as B receives i.e. $1000.

**(Ans: 2)**

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

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