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

**Problem**

**Problem**

A salesman’s terms are changed from a flat commission of 5% on all his sales to a fixed salary of $1000 plus 2.5% commission on all sales exceeding $4000. If his remuneration with the new scheme was $600 more than by the first scheme, what was his sales worth?

- $6000
- $9000
- $12000
- $15000
- $18000

**The Usual Method**

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Let the worth of sales be $‘*x*’

Hence income of salesman as per earlier scheme = 0.05*x*

And, income of sales man as per new scheme = 1000 + (*x* – 4000) x 0.025

Also, 1000 + (*x* – 4000) x 0.025 – 0.05*x* = 600

**(Ans: 3)**

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

**Using Technique**

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Just make a table as follows:

Sale Value Scheme I Scheme II Difference (II – I)

4000 200 1000+0 800

8000 400 1000+100 700

12000 600 1000+200 600

Hence the value of sale at which the difference is $600 is $12000.

**(Ans: 3)**

*Estimated Time to arrive at the answer = 30 seconds.*

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