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Percentages Smart Math

[Smart Math] Percentages Problem 18

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

Percentages

Problem

The cost for transportation amounts to 5% of the cost price. What is the cost price of goods sold for $1890 at 20% profit on the total outlay?

  1. $1417.50
  2. $1500
  3. $1575
  4. $1600
  5. $1675

The Usual Method

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Let the cost price of the goods be $‘x

Hence, price of goods after transportation = 1.05x

Adding 20% to it, we get: 1.20\times 1.05\times x

This is equal to $1890

1.20\times 1.05\times x=1890

\therefore x=\frac{1890}{1.20\times 1.05} = $1500

(Ans: 2)

Estimated Time to arrive at the answer = 45 seconds.

Using Technique

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Adding 20% on 100 is equivalent to removing 16.67% from 120. (as explained in the Percentages section of Stuff to Remember)

16.67% = \frac{1}{6} of the number

\therefore \frac{1}{6} of 1890 = 315.

Reducing 16.67% from 1890, we get 1890 – 315 = 1575

However, this is inclusive of transport cost of 5%

Hence, the actual answer is less by approximately 5%. The only option less than $1575 is $1500. Hence, option ‘2’. Note that $1417.50 is not the correct value since it is more than 5% less than 1575.

(Ans: 2)

Estimated Time to arrive at the answer = 15 seconds.
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