If price of an article decreases from Rs 800 to Rs 750, when quantity demanded increases from $Q_1$ units to 2250 units, and if point elasticity of demand is $-2$ find $Q_1$?

Given parameters:Initial Price ($P_1$) = $800$ New Price ($P_2$) = $750$ Change in price ($\Delta P$) = $750-800=-50$ Initial Quantity = $Q_1$ New Quantity ($Q_2$) = $2250$ Change in quantity ($\Delta Q$) = $2250-Q_1$ Elasticity of demand ($E_d$) = $-2$ Using the point elasticity formula:
$$E_d=\frac{\Delta Q}{\Delta P}\times \frac{P_1}{Q_1}$$
Substituting the values:
$$-2=\frac{2250-Q_1}{-50}\times \frac{800}{Q_1}$$
$$-2=\frac{2250-Q_1}{-1}\times \frac{16}{Q_1}$$
$$2=\frac{16(2250-Q_1)}{Q_1}$$
$$2Q_1=36000-16Q_1$$
$$18Q_1=36000$$
$$Q_1=\frac{36000}{18}=2000\text{units}$$