In this question
P=10
Q=20
p1=10-2=2
Q1=?

Ped=-Q1/P1*P/Q
==>-1=-Q1/2*10/20
==>Q1=4
==>New quantity is initial quantity+ Q1 = 20+4=24

So answer is 24

Price Elasticity of Demand

Price elasticity of demand measures the responsiveness of quantity demanded to a change in price. It indicates how sensitive consumers are to changes in price. The formula for price elasticity of demand is:

Price Elasticity of Demand = (% change in quantity demanded) / (% change in price)

A price elasticity of demand of -1 indicates that a 1% decrease in price will result in a 1% increase in quantity demanded, and vice versa.

Given Information

- Quantity demanded at a price of 10 rs. per unit = 20 units
- Price elasticity of demand = -1
- New price = 8 rs. per unit

Calculating Quantity Demanded

To calculate the quantity demanded when the price falls to 8 rs. per unit, we can use the price elasticity of demand formula. Let's assume the original price is P1 and the original quantity demanded is Q1, and the new price is P2.

% change in price = (P2 - P1) / P1 * 100

% change in quantity demanded = (Q2 - Q1) / Q1 * 100

We know that the price elasticity of demand is -1, so we can substitute the values into the formula and solve for Q2.

-1 = (% change in quantity demanded) / (% change in price)

-1 = (Q2 - Q1) / Q1 * 100 / (P2 - P1) / P1 * 100

Simplifying the equation:

-1 = (Q2 - Q1) / (P2 - P1)

Cross-multiplying:

Q2 - Q1 = - (P2 - P1)

Q2 = Q1 - (P2 - P1)

Q2 = 20 - (8 - 10)

Q2 = 20 + 2

Q2 = 22 units

Conclusion

When the price falls to 8 rs. per unit, the consumer would demand 22 units of the commodity. This can be explained by the price elasticity of demand, which indicates that a 1% decrease in price leads to a 1% increase in quantity demanded. In this case, the price decreased by 2 rs. per unit (20% decrease), resulting in an increase in quantity demanded of 2 units (10% increase). Therefore, the consumer would demand a total of 22 units when the price falls to 8 rs. per unit.