Profit Percentage Calculation for Article Y

This solution explains the step-by-step calculation to find the profit percentage on article Y, given the cost price, discounts, and profit details for article X.

Determine the Selling Price of Article X

The dealer buys article X for ₹1,000 and earns a profit of ₹337. Therefore, the selling price (SP) of article X is calculated as:

SP of X = Cost Price (CP) of X + Profit on X

SP of X = $₹1,000 + ₹337 = ₹1,337$

Calculate the Marked Price (MP)

Article X is sold after two successive discounts of 15% and 30%. The formula relating Selling Price (SP), Marked Price (MP), and discounts is:

SP = MP $\times$ (1 - Discount1) $\times$ (1 - Discount2)

Substituting the values for article X:

$₹1,337 = \text{MP} \times (1 - 0.15) \times (1 - 0.30)$

$₹1,337 = \text{MP} \times 0.85 \times 0.70$

$₹1,337 = \text{MP} \times 0.595$

Now, solve for MP:

MP = $₹1,337 / 0.595$

MP = $₹2,247.06$ (approximately)

Calculate the Selling Price of Article Y

Article Y has the same Marked Price (MP) as article X. It is sold at a single discount of 49%.

SP of Y = MP $\times$ (1 - Single Discount)

SP of Y = $₹2,247.06 \times (1 - 0.49)$

SP of Y = $₹2,247.06 \times 0.51$

SP of Y = $₹1,145.99$ (approximately ₹1,146)

Alternatively, using the exact fraction for MP:

SP of Y = $(₹1,337 / 0.595) \times 0.51 = ₹1,145.99...$

Calculate the Profit Percentage on Article Y

The Cost Price (CP) of article Y is ₹1,000.

Profit on Y = SP of Y - CP of Y

Profit on Y = $₹1,146 - ₹1,000 = ₹146$

The profit percentage is calculated as:

Profit Percentage on Y = $\frac{\text{Profit on Y}}{\text{CP of Y}} \times 100$

Profit Percentage on Y = $\frac{₹146}{₹1,000} \times 100$

Profit Percentage on Y = $0.146 \times 100 = 14.6\%$