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# Equivalent Discount

Discounts are offered to lure the customers. But many times shopkeepers offer multiple discounts to clear their goods. These successive equivalent discount are calculated on marked or selling price. Let us study them in detail.

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Discounts, as we all know, is the deduction on the price of the items. It is always calculated on the marked price. Similarly equivalent or successive discounts are more than one discount that is given to the customers. If the successive discounts d1, d2, and d3 are given on an item, then the selling price of that item is calculated by,

SP = (1 – d1/100) x (1 – d2/100) x (1 – d3/100) x MP, where SP is selling price and MP is marked price.

### Example Based on Successive Discounts

Q. The MRP of the product is given as Rs. 2000 and the merchant decides to provide successive discounts of 30% and 20% on the product. Find the selling price.

A. Rs. 1100          B. Rs. 1120             C. Rs. 1150                  D. Rs. 1200

You can see the similar type of questions asked in the competitive exams. Here, the important thing to remember is that in successive discount, first, you need to calculate the MRP after 30% discount and then whatever the answer you get should be used for calculating 20% discount.

Now, for the above question, the first discount will be, 30% of 2000 = Rs. 600. So, the discounted price will be 2000 – 600 = Rs. 1400. Now, on this, there is a further discount of 20%. So, the final discounted price will be 1400 – 20% of 1400 => 1400 – 280 = Rs. 1120. So, the final SP of the product will be Rs. 1120. Thus, the correct answer is B.

### Example Based on the Comparison of Discounts

Q. What will be more profitable from a customer’s point of view? Two successive discounts of 30% and 20% respectively or a single discount of 50%?

A. A single discount                        B. Two successive discounts
C. Either of the two                         D. Cannot be possible

Suppose that the market price of a product is Rs. 100. So for the case I two successive discounts of 30% and 20% are given respectively. So, the price after the first discount will be, 100 – 30% of 100 = 100 – 30 = Rs. 70. Now, the price after the second discount will be, 70 – 20% of 70 = 70 – 14 = Rs. 56. So, the customer has to pay Rs. 56 if he goes for the case I.

For case II there is a single discount of 50% given. So, final price after the single discount will be, 100 – 50% of 100 => 100 – 50 = Rs. 50. Thus, from both the cases we can conclude that the case II is Rs. 6 cheaper. So, the correct answer is A.

## Practice Questions

1. A merchant gives an additional discount of 10% on the product after an initial discount of 20% on the listed price. He managed to make a 10% profit by selling the product for Rs. 54,000. What was the listed price of the product?

A. Rs. 75,000            B. Rs. 72,500              C. Rs. 77,500                 D. Rs. 70,000

2. Jimmy decides to sell 40% of his old items at the market price, the remaining half at 20% discount and the rest of the items at two successive discounts of 20%. He marked the items such that he would earn 40% profit. Find his profit or loss percentage.

A. 1.8% profit               B. 1.8% loss                 C. 0.8% profit                  D. 0.8% loss

3. A shopkeeper wanted to sell Rs. 2000 worth of products. But he had two options, giving three successive discounts of 10% each or giving a single discount of 30%. What was the difference between the two options?

A. Rs. 56            B. Rs. 58                      C. Rs. 80                       D. Rs. 140

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