A shop owner offers the following discount options on an article to a customer : 1. Successive discounts of 10% and 20%, and then pay a service tax of 10% 2. Successive discounts of 20% and 10%, and then pay a service tax of 10% 3. Pay a service tax of 10% first, then successive discounts of 20% and 10% Which one of the following is correct?
- (a) 1 only is the best option for the customer.
- (b) 2 only is the best option for the customer.
- (c) 3 only is the best option for the customer.
- (d) All the options are equally good for the customer. ✓ UPSC's answer
Why the answer is (d)
• Let the marked price of the article be 100.
• For Option 1: A 10% discount reduces the price to 90; a subsequent 20% discount reduces it to 72; adding 10% service tax results in a final price of 79.2.
• For Option 2: A 20% discount reduces the price to 80; a subsequent 10% discount reduces it to 72; adding 10% service tax results in a final price of 79.2.
• For Option 3: Adding 10% service tax first increases the price to 110; a 20% discount reduces it to 88; a subsequent 10% discount reduces it to 79.2.
• Since the final price is 79.2 in all three scenarios, the options are mathematically equivalent.
• Therefore, all options are equally good for the customer, making option (d) correct.
Why the other options are wrong
- (a) 1 only is the best option for the customer.
- Option 1 is not uniquely the best because the final price is identical to the other options.
- (b) 2 only is the best option for the customer.
- Option 2 is not uniquely the best because the final price is identical to the other options.
- (c) 3 only is the best option for the customer.
- Option 3 is not uniquely the best because the final price is identical to the other options.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2020, held on 4 October 2020. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.