Gita sells two objects and at the same price such that she makes a profit of on object and loss of on object . If she increases the selling price such that objects and are still sold at an equal price and a profit of is made on object , then the profit made on object A will be nearest to
Gita sells two objects and at the same price such that she makes a profit of on object and loss of on object . If she increases the selling price such that objects and are still sold at an equal price and a profit of is made on object , then the profit made on object A will be nearest to
Solution
Gita has two objects A and B that she sells at equal prices in two different scenarios. We need to find how the profit on object A changes when she adjusts her selling strategy.
Key insight: When objects are sold at equal prices, we can set up equations using their cost prices and profit/loss percentages.
Let's define:
Cost Price of object A =
Cost Price of object B =
Object A: 20% profit means Selling Price = Cost Price + 20% of Cost Price
SP of A =
Object B: 10% loss means Selling Price = Cost Price - 10% of Cost Price
SP of B =
Since both objects are sold at the same price:
This equation tells us how the cost prices of A and B are related.
Now Gita increases the selling price so that:
Object B makes 10% profit: SP of B =
Objects A and B are still sold at equal prices
The ratio between the cost prices and remains the same, but the selling prices increase proportionally.
From the first scenario:
In the second scenario: SP of B =
Using proportions: If corresponds to , then corresponds to:
(approximately)
We're scaling up both selling prices by the same factor .
New SP of A =
Cost Price of A =
Profit on A = SP - CP =
Profit percentage =
Profit% =
Therefore, the profit on object A is approximately 47%.
Answer: 47%