A man bought a horse and a carriage for Rs. 3000. He sold the horse at a gain of 20% and the carriage at a loss of 10%, thereby gaining 2% on the whole. Find the cost of the horse. 

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Calculate the original cost of the horse in a scenario where a seller’s strategic moves result in a 2% overall profit despite varying gains and losses on individual items.

A man bought a horse and a carriage for Rs. 3000. He sold the horse at a gain of 20% and the carriage at a loss of 10%, thereby gaining 2% on the whole. Find the cost of the horse.

The cost of the Horse is Rs.1200.

Let’s denote the cost of the horse as H and the cost of the carriage as C.

According to the given conditions:

1. The man sold the horse at a gain of 20%, so he sold it for 120% of its cost.
2. The man sold the carriage at a loss of 10%, so he sold it for 90% of its cost.

Now, we can set up the equation for the total gain:

120% * H + 90% * C = 102% * (H + C)

Since the man bought both the horse and the carriage for Rs. 3000:

H + C = 3000

We have a system of two equations:

1. 1.2H + 0.9C = 1.02(H + C)
2. H + C = 3000

We can solve this system of equations to find the value of H (the cost of the horse).

From equation 2, we can express C = 3000 – H and substitute into equation 1:

1.2H + 0.9(3000 – H) = 1.02(3000)

1.2H + 2700 – 0.9H = 3060

0.3H + 2700 = 3060

0.3H = 3060 – 2700

0.3H = 360

H = 360 / 0.3

H = 1200

So, the cost of the horse was Rs. 1200.

System of Linear Equations in Algebra

Linear equations and systems of linear equations are fundamental concepts in algebra. Here’s a breakdown:

Linear Equation:

• An equation where the highest power of any variable is 1.
• Represents a straight line when graphed in two dimensions.
• Written in general form as ax + by = c, where a, b, and c are constants and x and y are variables.

System of Linear Equations:

• A collection of two or more linear equations involving the same variables.
• Represents a set of intersecting lines (or planes in higher dimensions).
• The solution is the set of values for the variables that satisfy all equations simultaneously.

Solving Systems of Linear Equations:

• Various methods exist, including:
  • Elimination (Gaussian elimination, Gauss-Jordan elimination)
  • Substitution
  • Matrix methods (using determinants or inverse matrices)
• The choice of method depends on the size and complexity of the system.

Applications of Systems of Linear Equations:

• Real-world problems involving multiple unknowns and relationships between them, such as:
  • Mixing chemicals with different concentrations
  • Balancing budgets with income and expenses
  • Analyzing motion with forces and velocities
  • Designing circuits with currents and voltages

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