An article is sold for 500 and hence a loss is incurred. Had the article been sold for 700, the shopkeeper would have gained three times the former loss. What is the cost price of the article?
Answers
Answer:
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Step-by-step explanation:
let us assume the cost price of the article is x.
CASE 1: When selling price is Rs 500
Selling price of article = Rs 500
Cost price of article = Rs x
Since loss has been incurred, Cost price > Selling price
Thus loss = Cost price - selling price = Rs (x - 500)
CASE 2: When selling price is Rs 700
Selling price of article = Rs 700
Cost price of article = Rs x
Since gain is incurred, Selling price > Cost price
Thus, gain = selling price - cost price = Rs ( 700- x)
According to question, Gain in case 2 = 3 x loss in case 1
Putting values that we have got,
700 - x = 3( x - 500 )
⇒ 700 - x = 3x - 1500
⇒ 3x + x = 700 + 1500
⇒ 4x = 2200
⇒ x = 550
Hence, cost price of the article is Rs 550.
CHECK:
Cost price = Rs 550
Selling price = Rs 500
Thus, loss = Rs 550 - 500 = Rs 50
When selling price = Rs 700
Gain = Rs 700 - 550 = Rs 150
We can see that Gain is 3 times of the loss incurred, which satisfies the given condition in the question.