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Percentages Smart Math

[Smart Math] Percentages Problem 29

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

Percentages

Problem

1 lb of sweets is marked at $100. Due to festival; a discount of 10% is given. Even after this discount, the shopkeeper earns 35% profit. What loss or gain would the shopkeeper make, if the sweets are sold for $30 less than the marked price?

  1. 5% loss
  2. 8% loss
  3. 5% gain
  4. 8% gain
  5. 3.33% gain

The Usual Method

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The marked price of sweets = $100

Selling price = $90 ( \because 10% discount was given)

Let the cost price be $‘x’.

Hence selling price with 35% profit = 1.35x = $90

\therefore x=\frac{90}{1.35}

Hence cost price = \frac{90}{135}\times 100=\frac{200}{3}

Now, if the sweets are sold at $30 less than the marked price i.e. at $70, the profit or loss = 70-\frac{200}{3}=\frac{210-200}{3}=\frac{10}{3}

Hence profit% = \frac{{}^{10}\!\!\diagup\!\!{}_{3}\;}{{}^{200}\!\!\diagup\!\!{}_{3}\;}\times 100= 5%

(Ans: 3)

Estimated Time to arrive at the answer = 60 seconds.

Using Technique

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Since the marked price is $100 discount of $30 is equivalent to discount of 30%. In the earlier discount of 10%, the profit was 35%, Hence, in the new discount of 30%, there will be some profit. However, this profit will be very little. Hence choose the least profit from the options.

(Note: This method may not work always. For e.g. if there is an option of 2% gain and if you mark that using this logic, you will get a wrong answer. However, this method does help to reduce the number of choices.)

(Ans: 3)

Estimated Time to arrive at the answer =10 seconds.
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