Question

A shopkeeper bought 150 books and sold 100 of them at a profit of 30% and the rest at 10% loss. if he had sold all the books at once at 25% profit, he would have received rs. 300 more. find the cost price of each book?

Answer 1

By setting up an equation based on the given profit margins and additional revenue, and then solving for x, we find that the cost price of each book is Rs. 24.

Step-by-step explanation:

The question involves a shopkeeper who bought 150 books and sold them at different profit margins. Let x be the cost price of each book. The shopkeeper sold 100 books at a 30% profit, so the selling price for these books is 100x(1 + 0.30). The remaining 50 books were sold at a 10% loss, so the selling price for these books is 50x(1 - 0.10). If all the books were sold at a 25% profit, the shopkeeper would have made an additional Rs. 300. This can be represented by the equation: 150x(1 + 0.25) = 100x(1 + 0.30) + 50x(1 - 0.10) + 300.

By solving this equation, we can find the cost price of each book:
150x(1.25) = 100x(1.30) + 50x(0.90) + 300
187.5x = 130x + 45x + 300
12.5x = 300
x = 300/12.5
x = 24

Therefore, the cost price of each book is Rs. 24.