If the price of an article decreases from Rs 100 to Rs 80, while the quantity demanded increases from Q
1
​
units to 4,600 units, and the point elasticity of demand is −0.75, find the value of Q
1
​
.

The formula for the price elasticity of demand using the percentage/proportional method is given by:
E
d
​
=
ΔP
ΔQ
​
×
Q
1
​

P
1
​

​

Where:

Initial Price (P
1
​
) = Rs 100

Final Price (P
2
​
) = Rs 80

Change in Price (ΔP) = P
2
​
−P
1
​
=80−100=−20

Initial Quantity = Q
1
​


Final Quantity (Q
2
​
) = 4600 units

Change in Quantity (ΔQ) = Q
2
​
−Q
1
​
=4600−Q
1
​


Price Elasticity of Demand (E
d
​
) = −0.75

Substituting the given values into the formula:

−0.75=
−20
4600−Q
1
​

​
×
Q
1
​

100
​

Simplify the expression:

−0.75=
−2
4600−Q
1
​

​
×
Q
1
​

10
​

−0.75=
−Q
1
​

5×(4600−Q
1
​
)
​

Multiply both sides by −Q
1
​
:

0.75×Q
1
​
=5×(4600−Q
1
​
)
0.75Q
1
​
=23000−5Q
1
​

Bring all Q
1
​
terms to one side:

0.75Q
1
​
+5Q
1
​
=23000
5.75Q
1
​
=23000
Q
1
​
=
5.75
23000
​

Q
1
​
=4000units