If price of an article decreases from Rs $P_1$ to Rs $150$, quantity demanded increases from $1000$ units to $1250$ units. If point elasticity of demand is $-1$, then find $P_1$?

Given parameters:Initial Quantity ($Q_1$) = $1000$ New Quantity ($Q_2$) = $1250$ Change in Quantity ($\Delta Q$) = $1250-1000=250$ New Price ($P_2$) = $150$ Initial Price = $P_1$ Change in Price ($\Delta P$) = $150-P_1$ Elasticity of Demand ($E_d$) = $-1$ Using the point elasticity of demand formula:
$$E_d=\frac{\Delta Q}{\Delta P}\times \frac{P_1}{Q_1}$$
Substitute the values into the formula:
$$-1=\frac{250}{150-P_1}\times \frac{P_1}{1000}$$
Simplify the fraction $\frac{250}{1000}=\frac{1}{4}$:
$$-1=\frac{1}{150-P_1}\times \frac{P_1}{4}$$
$$-1=\frac{P_1}{4(150-P_1)}$$
Cross-multiplying gives:
$$-4(150-P_1)=P_1$$
$$-600+4P_1=P_1$$
$$4P_1-P_1=600$$
$$3P_1=600$$
$$P_1=\frac{600}{3}=200$$
Thus, the initial price $P_1$ is Rs $200$.