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Percentages Smart Math

[Smart Math] Percentages Problem 24

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

Percentages

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?

  1. $6000
  2. $9000
  3. $12000
  4. $15000
  5. $18000

The Usual Method

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Let the worth of sales be $‘x

Hence income of salesman as per earlier scheme = 0.05x

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

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

\therefore 1000+0.025x-100-0.05x=600

\therefore 300=0.025x

\therefore x=\frac{300}{0.025}=\frac{300}{25}\times 1000=12000

(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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