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Percentages Smart Math

[Smart Math] Percentages Problem 28

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

Percentages

Problem

A salesman gets a flat commission of 10% on all sales and a bonus of 2.5% on all sales exceeding $10,000. If in a particular month he earns $2875, what were his sales worth?

  1. $35,000
  2. $23,000
  3. $25,000
  4. $15,000
  5. $24,000

The Usual Method

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Let the sales be worth $‘x’. (Assume x > $10,000)

Hence commission = \frac{10}{100}x=0.1x

And Bonus = \frac{2.5}{100}\times (x-10000)=0.025x-250

Hence total earnings = 0.1x+0.025x-250=2875

\therefore 0.125x=3125

\therefore x=\frac{3125}{0.125}= $25,000

(Ans: 3)

Estimated Time to arrive at the answer = 45 seconds.

Using Technique

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Since the total commission earned is more than $1000, ($2875), the sales has to be more than $10,000 (Since 10% of $10,000 = $1000). Hence any additional commission is attributable to sales worth over $10,000. Thus, 2875 – 1000 = 1875 is the commission earned on sales over $10,000. Note that the salesman continues to earn 10% commission along with the bonus of 2.5%. Hence total commission earned on sales over $10,000 = 10 + 2.5 = 12.5%. Thus $1875 is 12.5% of sales over $10,000. Hence, value of sale over $10,000 = \frac{1875}{12.5}\times 100= $15,000. Hence total sales are worth 10,000 + 15,000 = $25,000

(Ans: 3)

Estimated Time to arrive at the answer = 15 seconds.
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