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Finding Discounts and Sale Prices

The base for the calculation of discount or the rate of discount is always the list or marked price.

Let us understand this with some examples.
Example 11: If a geyser has a marked price of `6,000 and it is selling at a discounted price of `5,100,

find the rate of discount.
Solution: MP = `6,000 and the SP = `5,100

So, discount = `6,000 – `5,100 = `900

The per cent or rate of discount can be computed by using the formula,
Discount 900
Rate of discount = × 100% = × 100% = 15%
MP 6000

Example 12: The marked price of a smartwatch is `40,000. It is sold at a discount of 25%. Find the
selling price of the smartwatch.

Solution: The marked price of the smartwatch = `40,000 and percentage of discount = 25%

25
So, the amount of discount = 25% of `40,000 = × `40,000 = `10,000
100
So, the selling price of the smartwatch = Marked Price (MP) – Discount

= `40,000 – `10,000 = `30,000
 100 − Discount% 
Alternative Method: SP =   100   × MP

−
 100 25 75
=   × `40,000 = × `40,000 = `30,000
 100  100
Example 13: Find the marked price if the SP is `2337.50 and the rate of discount is 15%.
Solution: Here, SP = `2337.50 and the rate of discount = 15%

 100   100  100
So, MP =   × SP =   × `2337.50 = × `2337.50 = `2,750
 100 − Discount%   100 15 85
−
Example 14: A shopkeeper marks jeans at 30%
above the cost price and then allows a discount of Quick Check

10%. Does he gain 20% in this deal? A retailer marks his goods at 25% above the
Solution: Let CP = `100. cost price and then allows a discount of 20%.
What is his gain or loss per cent?
Then, MP = `100 + 30% of `100 = `130

−
 100 10 90
Now, SP after allowing a discount of 10% =   100   × `130 = 100 × `130 = `117
Now, gain = SP – CP = `117 – `100 = `17
17
And gain % = × 100 = 17%
100
Hence, he will not gain 20% in this deal.

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