Question

A shopkeeper sold two items, one at 25% profit and another at 15% loss and got a profit of 35rupees. If the cost price of the
item sold at 25% profit is twice than that of the item sold at 15% loss, find the sum of the cost price of both items.​

Answer 1

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Answer 2

The sum of the cost price of  both the items is Rs. 349.98.

• Let the cost price of the article sold at 15 % loss be x.

According to the given condition,

Cost price of the article sold at 25 %  profit = 2x

• Selling price of an article sold at a profit = { (100 + Profit %) / 100 } × C.P.

∴  Selling price of the article sold at 25 % profit = { (100 + 25) / 100 } × 2x

Or, S.P. of the first article = (125 / 100) × 2x

= (5 / 4) × 2x

= (5 × 2x) / 4

= 5x / 2

• Selling price of an article sold at a loss = { (100 - Loss %) / 100 } × C.P.

∴   Selling price of the article sold at 15 % loss = { ( 100 - 15) / 100 } × x

Or, S.P. of the second article = (85 / 100) × x

= (17 / 20) × x

= (17 × x) / 20

= 17x / 20

• Now, the total selling price of two articles = (5x / 2) + (17x / 20)

= ( 5x × 10 + 17x × 1 ) / 20

= (50x + 17x) / 20

= 67x / 20

• Given that, total profit earned on both the articles = Rs. 35

Now, Total Profit = Total S.P. - Total C.P.

• Total C.P. of the two articles = x + 2x = 3x

• Therefore,

Rs. 35 = (67x / 20) - 3x

Or, Rs. 35 = (67x - 3x × 20) / 20

Or, Rs. 35 = (67x - 60x) / 20

Or, Rs. 35 = 6x / 20

Or, x = (Rs. 35 × 20) / 6x

Or, x = (Rs. 35 × 10) / 3x

Or, x = Rs. 350 / 3x

Or, x = Rs. 116.66

• Now, the cost price of the article sold at a loss of 15 % = Rs. 116.66

Cost price of the article sold at a profit of 25 % = 2× Rs. 116.66 = Rs. 233.32

• Total cost price of both the articles = Rs. 116.66 + Rs. 233.32

= Rs. 349.98