A person sells article X for ₹34,500 and makes a profit of 15%. He sells article Y at a loss of 10%. He neither loses nor gains on the whole because of these two transactions. What is the selling price of article Y?

Given:

Profit on article X = 15%

Selling price of article X = ₹34,500

Loss on article Y = 10%

No overall gain or loss (Net profit = ₹0)

Formula used:

Cost price (CP) = \(\frac{\text{Selling Price (SP)}}{1+\frac{\text{Profit%}}{100}}\)

Cost price (CP) = \(\frac{\text{Selling Price (SP)}}{1-\frac{\text{Loss%}}{100}}\)

Calculations:

For article X:

CP of article X = \(\frac{34500}{1+\frac{15}{100}}\)

⇒ CP of article X = \(\frac{34500}{1.15}\)

⇒ CP of article X = ₹30,000

For article Y:

Total cost price of X and Y = Total selling price of X and Y

⇒ CP of X + CP of Y = SP of X + SP of Y

⇒ ₹30,000 + CP of Y = ₹34,500 + SP of Y

⇒ CP of Y = SP of Y - ₹4,500

CP of article Y = \(\frac{\text{SP of Y}}{1-\frac{10}{100}}\)

⇒ SP of Y - ₹4,500 = \(\frac{\text{SP of Y}}{0.9}\)

⇒ 0.9(SP of Y - ₹4,500) = SP of Y

⇒ 0.9SP of Y - ₹4,050 = SP of Y

⇒ SP of Y - 0.9SP of Y = ₹4,050

⇒ 0.1SP of Y = ₹4,050

⇒ SP of Y = ₹4,050 × 10

⇒ SP of Y = ₹40,500

∴ The correct answer is option (2).