If price of an article decreases from Rs P
1
​
to Rs 240, when quantity demanded increases from 8000 units to 8400 units, and if point elasticity of demand is −1.25 find P
1
​
?

The formula for the price elasticity of demand (E
d
​
) using the percentage/proportional method is:

E
d
​
=
ΔP
ΔQ
​
×
Q
1
​

P
1
​

​

Given:

Initial quantity (Q
1
​
) = 8000 units

New quantity (Q
2
​
) = 8400 units

Change in quantity (ΔQ) = Q
2
​
−Q
1
​
=8400−8000=400

Initial price = P
1
​


New price (P
2
​
) = 240

Change in price (ΔP) = P
2
​
−P
1
​
=240−P
1
​


Elasticity of demand (E
d
​
) = −1.25

Substituting the values into the formula:

−1.25=
240−P
1
​

400
​
×
8000
P
1
​

​

Simplifying the fraction:

−1.25=
8000
400
​
×
240−P
1
​

P
1
​

​

−1.25=
20
1
​
×
240−P
1
​

P
1
​

​

Multiplying both sides by 20:

−1.25×20=
240−P
1
​

P
1
​

​

−25=
240−P
1
​

P
1
​

​

Cross-multiplying:

−25(240−P
1
​
)=P
1
​

−6000+25P
1
​
=P
1
​

25P
1
​
−P
1
​
=6000
24P
1
​
=6000
P
1
​
=
24
6000
​
=250
Thus, the initial price P
1
​
is Rs 250.