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Percentages Smart Math

[Smart Math] Percentages Problem 14

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

Percentages

Problem

An article is sold at a profit of 20%. If both the cost price and selling price were to be $20 less, the profit made would be 10% more. What is the cost price of the article?

  1. $30
  2. $40
  3. $50
  4. $60
  5. $70

The Usual Method

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Let the cost price of the article be $x.

Hence selling price = 1.2x

Reduced cost price = (x – 20)

Reduced selling price = (1.2x – 20)

Hence, profit % = \frac{\left( 1.2x-20 \right)-\left( x-20 \right)\times 100}{\left( x-20 \right)} = 20% + 10% = 30%

\therefore \frac{\left( 1.2x-20-x+20 \right)\times 100}{\left( x-20 \right)}=30

\therefore 0.2x\times 100=30(x-20)

\therefore 10x=600

\therefore x=60 = Cost price

(Ans: 4)

Estimated Time to arrive at the answer = 60 seconds.

Using Technique

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As can be seen that by a reduction in cost price, there is an increase in profit %. The increase in profit % = \frac{10\times 100}{20}=50%

So, for a 50% increase, there should be a 33.33% reduction in cost price (as explained in the Percentages section of Stuff to Remember)

Hence, the original cost price should be such that a reduction of $20 is equivalent to a reduction of 33.33%.

Hence, original cost price = \frac{20\times 100}{33.33}=60

(Ans: 4)

Estimated Time to arrive at the answer = 10 seconds.
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