A fan is listed at Rs. 150 and is offered to customers at a first discount of 20%; what additional discount on the reduced price must be given so that the final net selling price becomes Rs. 108?

Introduction / Context:
This question tests the concept of successive discounts. A product is first discounted by a certain percentage on its list price and then an additional discount is applied on the already reduced price. The final selling price is known, and we must determine the second discount. A key point is that successive discounts do not simply add the percentages, because each discount is applied on a different base price.

Given Data / Assumptions:

• List price of the fan is Rs. 150.
• First discount is 20% on the list price.
• After both discounts, net selling price should be Rs. 108.
• We must find the second discount percentage applied on the reduced price after the first discount.
• The second discount is applied on the already reduced price, not on the original price.

Concept / Approach:
First we compute the price after the initial 20% discount. Then we assume the second discount rate as d percent on this reduced price and form an equation equating the final price to Rs. 108. From this equation we determine the value of d. Finally, we compare the obtained value with the options. If none of the options match exactly, the correct choice is "None of these". This shows the importance of calculating precisely rather than selecting approximate values.

Step-by-Step Solution:
Marked price (list price) of the fan is Rs. 150.First discount is 20%, so price after first discount = 150 * (1 - 0.20) = 150 * 0.8 = Rs. 120.Let the additional discount on Rs. 120 be d%.Then net price after second discount = 120 * (1 - d / 100).We are told that this final net price must be Rs. 108.So 120 * (1 - d / 100) = 108.Divide both sides by 120: 1 - d / 100 = 108 / 120 = 0.9.Thus d / 100 = 0.1 so d = 10%.

Verification / Alternative check:
Confirm with actual prices. After first discount, price is 120. If second discount is 10%, then discount amount is 10% of 120 that is 12, so final price is 120 - 12 = 108. This matches the required final selling price. Therefore the correct additional discount is exactly 10%. Since the options list 11 1/9%, 15%, 8%, and None of these, and 10% is not present, the only correct option is "None of these".

Why Other Options Are Wrong:
11 1/9% would produce a second discount of about 13.33 on 120, resulting in a final price different from 108.

15% would reduce 120 by 18, giving a final price of 102, which is too low.

8% would reduce 120 by 9.6 to 110.4, which is higher than 108 and not acceptable.

Common Pitfalls:
A common mistake is to think that an overall discount from 150 to 108 is 42 rupees, which is 28% of 150, and then assume the second discount is 8% because 20% plus 8% equals 28%. This ignores the fact that the second discount applies to 120, not to 150. Another pitfall is misreading the question to think that the second discount is also on the list price. Always identify the exact base to which each percentage is applied and set up equations accordingly.

Final Answer:
The required additional discount is 10%, which is not listed among the numerical options, so the correct choice is None of these.