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Percentages Smart Math

[Smart Math] Percentages Problem 31

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

Percentages

Problem

A housewife reduces her consumption of coffee by 20% due to a 20% increase in price of coffee. What is the percentage effect on the expenditure on coffee?

  1. 4% increase
  2. 2% increase
  3. No change
  4. 2% decrease
  5. 4% decrease

The Usual Method

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Assuming the original price of coffee as $100/unit

So new price = $120/unit (20% increase)

Let the consumption be 100 units

New consumption = 80 units (20% decrease)

Original expenses of coffee = 100 x 100 = $10,000

New expenses of coffee = 80 x 120 = $9600

Hence, change = $10,000 – $9600 = $400

Hence percentage change = \frac{400}{10000}\times 100=4% decrease.

(Ans: 5)

Estimated Time to arrive at the answer = 45 seconds.

Using Technique

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From the table of % in the section of Percentages in Stuff to Remember, we note that if the rate of coffee increases by 20% in order to maintain the same expenses, the consumption should be reduced by 16%. But actually, the consumption is reduced by 20%. Hence the net effect is 4% (20 – 16 = 4) decrease in expenses.

(Ans: 5)

Estimated Time to arrive at the answer = 5 seconds.
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