# Q. A shop owner offers the following discount options on an article to a customer:

1. Successive discounts or 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 or 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.

Correct Answer: (d) All the options are equally good for the customer.

#### Question from UPSC Prelims 2020 CSAT Paper

**Explanation :**

## Article’s Final Price Calculations

Let’s calculate the effective discount for each option, assuming the original price of the article is P.

**Option 1:**

First discount: 10% -> P * (1 – 0.10) = 0.9P

Second discount: 20% -> 0.9P * (1 – 0.20) = 0.9P * 0.8 = 0.72P

Service tax: 10% -> 0.72P * (1 + 0.10) = 0.72P * 1.1 = 0.792P

**Option 2:**

First discount: 20% -> P * (1 – 0.20) = 0.8P

Second discount: 10% -> 0.8P * (1 – 0.10) = 0.8P * 0.9 = 0.72P

Service tax: 10% -> 0.72P * (1 + 0.10) = 0.72P * 1.1 = 0.792P

**Option 3:**

Service tax: 10% -> P * (1 + 0.10) = 1.1P

First discount: 20% -> 1.1P * (1 – 0.20) = 1.1P * 0.8 = 0.88P

Second discount: 10% -> 0.88P * (1 – 0.10) = 0.88P * 0.9 = 0.792P

All three options result in the customer paying the same final price, which is 79.2% of the original price (0.792P). So, all options are equivalent in terms of the final price for the customer.