A book seller allows a 10% discount on the printed price of a book and receives a 30% commission from the publisher on that printed price. What percentage profit does the book seller make on the deal?

Introduction / Context:
This question combines two commercial concepts: trade discount to customers and commission from the publisher. The book seller gets a commission on the printed price but also gives a discount to the buyer. The net effect on profit can be found only by carefully tracking all money flows. Such problems are common in aptitude tests focused on profit and loss and commercial arithmetic.

Given Data / Assumptions:

• Printed price (marked price) of the book is M rupees.
• Book seller allows 10% discount to the customer, so the customer pays 90% of M.
• The book seller gets 30% commission from the publisher on M.
• We assume there are no other costs.
• We need to find the overall profit percentage of the book seller.

Concept / Approach:
The idea is:

• The customer pays selling price SP = 0.9M.
• The publisher gives commission = 0.3M to the seller.
• The money which effectively goes from seller to publisher is M - 0.3M = 0.7M, which behaves like cost price for the seller.
• Effective cost price CP for the seller = 0.7M.
• Effective selling price SP for the seller = 0.9M (amount collected from customer).
• Profit percent = ((SP - CP) / CP) * 100.

Step-by-Step Solution:
Let printed price (marked price) be M. Customer pays 10% less, so SP = 0.9M. Seller gets 30% commission from publisher, that is 0.3M. Amount remitted by seller to publisher = M - 0.3M = 0.7M. This 0.7M is effectively the cost price CP for the seller. Thus CP = 0.7M and SP = 0.9M. Profit = SP - CP = 0.9M - 0.7M = 0.2M. Profit percent = (0.2M / 0.7M) * 100 = (2 / 7) * 100. (2 / 7) * 100 = 28.5714%, which is 28 4/7% approximately.

Verification / Alternative check:
Take a simple value, for example M = Rs 100. Then:

• Customer pays RS 90 (10% discount).
• Publisher allows 30% commission, so seller remits only Rs 70 to publisher.
• Effective cost price = 70, selling price = 90, profit = 20.
• Profit percent = (20 / 70) * 100 = 28.5714% = 28 4/7%.

This matches the result from algebra. Therefore, the answer is correct.

Why Other Options Are Wrong:
20% assumes profit is simply 10% of printed price, ignoring commission. Options 25% and 26 3/7% underestimate the real impact of the commission and discount combined. 18% is even smaller and does not match any logical combination. Only 28 4/7% correctly reflects the net margin after considering both discount and commission.

Common Pitfalls:
Many learners treat the 30% commission as extra profit without seeing that it also changes the effective cost to the seller. Others use the customer price as cost and get wrong percentages. Always identify who pays what to whom and treat what the seller finally pays out as cost price, and what the seller receives from the customer as selling price.

Final Answer:
The book seller makes a profit of 28 4/7% on the book.