Amar bought three articles A, B and C at a price ratio of 2 : 3 : 4 respectively. The total cost was ₹ 81,000. If all the three articles A, B and C were sold for ₹ 1,20,000 at a selling price ratio of 7 : 8 : 9 respectively, then what is the percentage profit he earned by selling A and C?

Given:

Price ratio of A, B, and C = 2 : 3 : 4

Total cost = ₹ 81,000

Selling price ratio of A, B, and C = 7 : 8 : 9

Total selling price = ₹ 1,20,000

Formula Used:

Percentage Profit = \(\frac{Selling Price - Cost Price}{Cost Price} \times 100\)

Calculation:

Let the cost price of A be 2x, B be 3x, and C be 4x.

⇒ 2x + 3x + 4x = 81,000

⇒ 9x = 81,000

⇒ x = 81,000 / 9

⇒ x = 9,000

Cost price of A = 2x = 2 × 9,000 = ₹ 18,000

Cost price of C = 4x = 4 × 9,000 = ₹ 36,000

Let the selling price of A be 7y, B be 8y, and C be 9y.

⇒ 7y + 8y + 9y = 1,20,000

⇒ 24y = 1,20,000

⇒ y = 1,20,000 / 24

⇒ y = 5,000

Selling price of A = 7y = 7 × 5,000 = ₹ 35,000

Selling price of C = 9y = 9 × 5,000 = ₹ 45,000

Total cost price of A and C = 18,000 + 36,000 = ₹ 54,000

Total selling price of A and C = 35,000 + 45,000 = ₹ 80,000

Percentage Profit = \(\frac{80,000 - 54,000}{54,000} \times 100\)

⇒ Percentage Profit = \(\frac{26,000}{54,000} \times 100\)

⇒ Percentage Profit = \(\frac{26}{54} \times 100\)

⇒ Percentage Profit = 48.15%

The correct answer is option 1.