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# [Smart Math] Percentages Problem 29

Here’s and example of a SMART MATH problem for 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

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

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.