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A trader bought two goats for Rs. 18000. He sold one at a loss of 25% and other at a profit of 25%. If the selling price of each goat is same, then the ratio of their cost prices is 
1. 5 ∶ 4
2. 4 ∶ 5
3. 5 ∶ 3
4. 3 ∶ 5

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Correct Answer - Option 3 : 5 ∶ 3

Given:

Cost price of both goats = Rs. 18000

Loss on first goat = 25%

Profit on second goat = 25%

Formula Used:

Loss % = ((CP - SP)/CP) × 100%

Profit % = ((SP - CP)/CP) × 100%

Calculation:

Let the cost prize of first goat = Rs. x

and the cost prize of second goat = Rs. y

Let the selling prize of each goat = Rs. z

Loss on first goat = 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 goat = 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.

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