Profit on the sale of 10 cups is same as the selling price of 3 glasses. Loss on selling 10 glasses equals selling price of 4 cups. Also profit percentage in the above deal equals the loss percentage and cost of a cup is half of the cost of a glass. What is the ratio of selling price of a cup to the selling price of a glass?
Answers
Given : Profit on the sale of 10 cups is same as the selling price of 3 glasses. Loss on selling 10 glasses equals selling price of 4 cups. Also profit percentage in the above deal equals the loss percentage and cost of a cup is half of the cost of a glass.
To find : What is the ratio of selling price of a cup to the selling price of a glass
Solution:
cost of a cup is half of the cost of a glass
=> Cost of Cup = C
Then Cost of Glass = 2C
Let say Profit % = Loss % = x
Profit on Selling 1 Cup = (x/100)C = Cx/100
Selling Price of 1 Cup = C + Cx/100
Loss on Selling 1 Glass = (x/100)2C = 2Cx/100
Selling Price of Glass = 2C - 2Cx/100
Profit on the sale of 10 cups is same as the selling price of 3 glasses
=> 10 (Cx/100) = 3(2C - 2Cx/100)
=> 10Cx = 3(200C - 2Cx)
=> 10Cx = 600C - 6CX
=> 16Cx = 600C
=> x = 75/2
Loss on selling 10 glasses equals selling price of 4 cups.
=> 10(2Cx/100) = 4(C + Cx/100)
=> 20Cx = 4(100C + Cx)
=> 20Cx = 400C + 4Cx
=> 16Cx = 400C
=> x = 25
Hence There are mistake in data
as Loss % & Profit % could not be equal with given Data if cost of a cup is half of the cost of a glass
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