If the demand curve for roller skates is given by D = 23000 - 19P and the supply curve is given by S = 18000 + 6P, what is the equilibrium price (P) of roller skates in rupees?

Introduction / Context:
This question tests the student's understanding of equilibrium in a simple linear demand and supply framework. In microeconomics, the equilibrium price is found where the quantity demanded equals the quantity supplied. Here, both demand and supply are expressed as linear functions of price. Solving such equations is common in Indian economy and basic microeconomics questions, and it reinforces algebra skills and conceptual clarity about market equilibrium.

Given Data / Assumptions:
- Demand function: D = 23000 - 19P.
- Supply function: S = 18000 + 6P.
- P represents price in rupees per pair of roller skates.
- Equilibrium occurs where quantity demanded equals quantity supplied, that is D = S.
- We assume a perfectly competitive market with no other distortions.

Concept / Approach:
The basic concept is that market equilibrium is reached when the quantity consumers wish to buy equals the quantity producers wish to sell. Mathematically, this means setting the demand equation equal to the supply equation and solving for the price P. Once the equilibrium price is obtained, one could also compute the equilibrium quantity, but the question asks only for the price level. This type of problem typically requires solving a pair of linear equations with one unknown.

Step-by-Step Solution:
Step 1: Write the equilibrium condition by setting demand equal to supply: 23000 - 19P = 18000 + 6P. Step 2: Bring all terms involving P to one side and constants to the other side. Subtract 18000 from both sides: 23000 - 18000 - 19P = 6P. Step 3: Simplify the constants: 5000 - 19P = 6P. Step 4: Add 19P to both sides to group P terms: 5000 = 6P + 19P = 25P. Step 5: Solve for P by dividing both sides by 25: P = 5000 / 25 = 200. Step 6: Therefore, the equilibrium price of roller skates is 200 rupees.

Verification / Alternative check:
To verify, substitute P = 200 into both the demand and supply equations. Demand at P = 200 is D = 23000 - 19 * 200 = 23000 - 3800 = 19200 units. Supply at P = 200 is S = 18000 + 6 * 200 = 18000 + 1200 = 19200 units. Since D and S are equal at 19200 units when P = 200, the condition for equilibrium is satisfied. No other given option leads to such equality, so Rs 200 is confirmed as the correct equilibrium price.

Why Other Options Are Wrong:
Rs 100 is wrong because substituting P = 100 would give demand and supply quantities that do not match, so the market is not in equilibrium.
Rs 400 is wrong because at that price the demand would be much lower and supply much higher, again violating the equilibrium condition.
Rs 50 is wrong for the same reason: it leads to a mismatch between quantity demanded and quantity supplied, with demand exceeding supply at a very low price.

Common Pitfalls:
Students often make algebraic errors when moving terms across the equality sign, especially with negative coefficients. Another common mistake is to forget that both demand and supply are functions of the same price variable, and therefore they must be equated, not added. It is also important to carefully check calculations like 23000 minus 3800 or 18000 plus 1200, since even small arithmetic mistakes can lead to a wrong answer despite correct method. Systematically writing each step and double checking the arithmetic helps avoid such errors in the exam.

Final Answer:
The equilibrium price of roller skates, where demand equals supply, is Rs 200.