On selling a pen at loss and a book at gain, Karim gains Rs. . If he sells the pen at gain and the book at gain, he gains Rs. 13. What is the cost price of the book in Rupees?
On selling a pen at loss and a book at gain, Karim gains Rs. . If he sells the pen at gain and the book at gain, he gains Rs. 13. What is the cost price of the book in Rupees?
Solution
We have two items: a pen and a book. Karim sells them under different conditions and gets different total gains. We need to find the cost price of the book.
When we sell something at a gain or loss, the selling price changes based on the cost price:
At 5% loss: Selling Price = 95% of Cost Price = 0.95 × Cost Price
At 15% gain: Selling Price = 115% of Cost Price = 1.15 × Cost Price
Let's define:
Cost Price of Pen = rupees
Cost Price of Book = rupees
Condition 1: Pen at 5% loss, Book at 15% gain → Total gain = Rs. 7
Selling Price of Pen = (since 5% loss means he gets 95% of cost price)
Selling Price of Book = (since 15% gain means he gets 115% of cost price)
Total Selling Price =
Total Cost Price =
Total Gain = Total Selling Price - Total Cost Price = 7
Therefore:
... (Equation 1)
Condition 2: Pen at 5% gain, Book at 10% gain → Total gain = Rs. 13
Selling Price of Pen = (since 5% gain means he gets 105% of cost price)
Selling Price of Book = (since 10% gain means he gets 110% of cost price)
Following the same logic:
... (Equation 2)
We have:
Equation 1:
Equation 2:
Notice that the coefficients of are opposites (-0.05 and +0.05). When we add these equations, the terms will cancel out.
Adding Equation 1 and Equation 2:
The terms cancel:
We get:
Therefore:
The cost price of the book is Rs. 80.
When solving profit-loss problems with multiple items, we set up equations using the relationship: Selling Price = Cost Price × (1 ± percentage/100), then use the given total gains to form a system of equations.