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I stumbled upon a simple question yet got it incorrect.

Jacob bought a scooter for a certain sum of money. He spent 10% of the cost on repairs and sold the scooter for a profit of Rs 1100. How much did he spend on repairs if he made a profit of 20% ?

My attempt:

Assuming initial cost price as CP (price at which Jacob purchased the scooter)

Repairs=0.1*CP

CP+ 0.1CP + Profit = Selling price

1.1*CP + 1100 = 1.2 * CP ?

CP= 11000

Repairs= 0.1 * 11000 = 1100

The equation marked with a "?" is where i have a doubt. I need to take 20% profit on the cost price, so do i take it on the original cost price i.e. 1.2*CP or on the cost incurred by Jacob before selling i.e. 1.1*CP*1.2 ?

How is this decided?

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1  
If you buy something for $4$ and sell it for $5$, you have made $1$ profit, which is either a $25$% profit on your investment or a $20$% profit on the purchase price. So it depends on what you mean by "he made a 20% profit." –  Thomas Andrews Oct 10 '12 at 17:10

2 Answers 2

up vote 2 down vote accepted

Use simple unitary method.

Let the price at which Jacobs bought the scooter (C.P) be Rs. 100. He spent Rs. 10 on repairs, so that makes the total cost to be Rs. 110.

He sold the scooter at a 20% profit, and 20% of 110 is 22, so he sold the scooter at a profit of Rs. 22.

Now, when the CP is Rs. 100, the profit is Rs. 22. When the profit is Rs. 1100, the CP is $$CP=\frac{1100*100}{22}=Rs. 5,000$$ Therefore, he spent Rs. 500 on repairs. It is assumed that the cost of the repairs is added to the original cost price of the scooter and the profit percentage is calculated on this price and not the original cost price.

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In the old old days before there were any $x$, reasoning like the one above was a standard tool. I think of the above as a better way than writing down equations, because one retains concrete control of the situation. Introducing algebraic formalism has the disadvantage that all formulas "look alike." The formalism is essential for complex problems, but may be counterproductive in simpler cases. –  André Nicolas Oct 10 '12 at 17:15

There is some ambiguity in what $20\%$ profit means in this case. But if J. is a businessperson and does not count the repairs as costs, he will quickly be out of business. So in answer to your question, I think the most reasonable interpretation of $20\%$ is $20\%$ of total investment (initial cost plus repairs).

Let the cost be $x$. Then $$1100=(0.2)(1.1x).$$

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here its considered that he takes the cost of repairs into account and adds that to his original cost price. –  Ayush Khemka Oct 10 '12 at 17:02
    
@Andre Yeah, it seems a bit ambiguous. Thanks. –  Karan Oct 10 '12 at 17:58

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