Correct Answer - Option 3 : 5 ∶ 3
Given:
Cost price of both chairs = Rs. 18000
Loss on first chair = 25%
Profit on second chair = 25%
Formula Used:
Loss % = ((CP - SP)/CP) × 100%
Profit % = ((SP - CP)/CP) × 100%
Calculation:
Let the cost prize of first chair = Rs. x
and the cost prize of second chair = Rs. y
Let the selling prize of each chair = Rs. z
Loss on first chair = 25%
Loss % = ((CP - SP)/CP) × 100%
⇒ 25 = ((x - z)/x) × 100
⇒ 1/4 = (x - z)/x
⇒ x = 4(x - z)
⇒ x = 4x - 4z
⇒ 3x = 4z
⇒ x = (4/3)z
Profit on second chair = 25%
Profit % = ((SP - CP)/CP) × 100%
⇒ 25 = ((z - y)/y) × 100
⇒ 1/4 = (z - y)/y
⇒ y = 4(z - y)
⇒ y = 4z - 4y
⇒ 5y = 4z
⇒ y = (4/5)z
Required ratio = x ∶ y
⇒ Required ratio = (4/3)z ∶ (4/5)z
⇒ Required ratio = 5 ∶ 3
∴ The ratio of their cost prices is 5 ∶ 3.