The demand curve for Alphonso mangoes is D = 25000 - 70P and the supply curve is S = 10000 + 80P, where P is price and D and S are quantities. What is the equilibrium quantity (in units) where demand equals supply?

Introduction / Context:
Even though this question appears under physics, it is actually a simple microeconomics problem about market equilibrium. The demand and supply of Alphonso mangoes are given as linear functions of price. The equilibrium point in a competitive market occurs where the quantity demanded equals the quantity supplied. This question asks you to find the corresponding equilibrium quantity.

Given Data / Assumptions:

• Demand function: D = 25000 - 70P.
• Supply function: S = 10000 + 80P.
• P represents the price per unit (exact currency units are not specified).
• Equilibrium occurs when D = S.
• We assume all quantities are in the same units (for example, kilograms or number of units).

Concept / Approach:
In a simple linear demand-supply model, equilibrium is found by solving the equation D = S for the price P and then substituting this price back into either the demand or supply function to obtain the equilibrium quantity. Algebraically, this becomes solving a single linear equation in one variable. Careful handling of signs is important because demand typically slopes downward with price (negative coefficient for P), while supply slopes upward (positive coefficient for P).

Step-by-Step Solution:
Step 1: Set demand equal to supply for equilibrium: 25000 - 70P = 10000 + 80P. Step 2: Bring like terms together: 25000 - 10000 = 80P + 70P. Step 3: Simplify the left side: 15000 = 150P. Step 4: Solve for price: P = 15000 / 150 = 100. Step 5: Substitute P = 100 into the demand function to get equilibrium quantity: D = 25000 - 70 * 100. Step 6: Compute D: 70 * 100 = 7000, so D = 25000 - 7000 = 18000 units. This equals the supply at equilibrium as well.

Verification / Alternative check:
Check with the supply equation: S = 10000 + 80 * 100 = 10000 + 8000 = 18000 units, which matches the demand at price 100. Since both demand and supply give 18000 units at this price, the equilibrium quantity is confirmed as 18000 units. Additionally, the demand curve slope is negative (coefficient -70) and the supply curve slope is positive (coefficient +80), so they intersect exactly once, giving a unique equilibrium.

Why Other Options Are Wrong:
2,000 units, 1,800 units and 200 units: These values do not satisfy both the demand and supply equations at any common price. They likely result from algebraic errors such as misplacing zeros, ignoring the minus sign in the demand equation or miscomputing the product 70 * 100.

Common Pitfalls:
A common mistake is to forget the minus sign in the demand equation and treat it as D = 25000 + 70P, which would give an incorrect equilibrium. Another frequent error is to solve for quantity directly without first solving for price, leading to confusion between variables. To avoid this, always set D = S, solve for P carefully and then use that value to compute the equilibrium quantity.

Final Answer:
The equilibrium quantity of Alphonso mangoes is 18,000 units.