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.**