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.