Two horses were bought at ₹ 1600. First was sold at 10% profit and second at 20% profit. If first were sold at 20% profit and second at 10% profit he would get ₹ 5 more. Find the d... Two horses were bought at ₹ 1600. First was sold at 10% profit and second at 20% profit. If first were sold at 20% profit and second at 10% profit he would get ₹ 5 more. Find the difference between the cost price of both the horses.
Understand the Problem
The question is asking us to determine the difference in the cost price of two horses bought for a total of ₹1600, where one was sold at a profit of 10% and the other at a profit of 20%. The question also provides information about alternative scenarios where profit margins are switched, aiming to find the difference in their cost prices based on the conditions given.
Answer
The difference in cost prices is ₹50.
Answer for screen readers
The difference in the cost price of both horses is ₹50.
Steps to Solve
- Define Variables for Cost Prices
Let the cost price of the first horse be $x$ and the second horse be $y$. The total cost price is given by the equation:
$$ x + y = 1600 $$
- Set Up Profit Equations for the First Scenario
For the first horse sold at a 10% profit:
$$ \text{Selling Price}_1 = x + 0.1x = 1.1x $$
For the second horse sold at a 20% profit:
$$ \text{Selling Price}_2 = y + 0.2y = 1.2y $$
- Set Up Profit Equations for the Alternate Scenario
If the first horse is sold at a 20% profit and the second at 10%, then:
$$ \text{Selling Price}_1' = x + 0.2x = 1.2x $$
$$ \text{Selling Price}_2' = y + 0.1y = 1.1y $$
- Establish the Difference in Selling Prices
According to the problem, if sold in the alternate way, he would get ₹5 more. This leads to the equation:
$$ 1.2x + 1.1y = 1.1x + 1.2y + 5 $$
- Simplify the Equation
Rearranging gives:
$$ 0.1x - 0.1y = 5 $$
Dividing through by 0.1:
$$ x - y = 50 $$
- Solve the System of Equations
Now we have two equations:
-
$x + y = 1600$
-
$x - y = 50$
Adding these two equations:
$$ 2x = 1650 \implies x = 825 $$
Using $x$ to find $y$:
$$ 825 + y = 1600 \implies y = 775 $$
- Calculate the Difference in Cost Prices
Finally, to find the difference between the cost prices:
$$ |x - y| = |825 - 775| = 50 $$
The difference in the cost price of both horses is ₹50.
More Information
This problem involves the application of profit percentage and algebraic equations. The relationships between selling prices and cost prices help to establish two equations with two variables, which can be solved simultaneously.
Tips
- Miscalculating percentages when setting up selling price equations.
- Forgetting to rearrange equations correctly when combining them.
- Not properly interpreting the profit scenarios, leading to incorrect setups.
