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This is a question that is much easier than it first appears. If you work with the percents directly, you can solve it very quickly. If the man sells 32 oranges for a dollar, he loses 40%. That means he is at 60% of his cost (100% - 40% = 60%). We are trying to figure out how many oranges he has to sell in order to make a 20% profit, or be at 120% (100% + 20% = 120%). 120% is double 60%, meaning that we simply cut the number of oranges in half to double our returns (from 60% to 120%), yielding 32/2 = 16 oranges, or answer choice A.

You can use the relation between Cost Price & Selling Price to get to your answer.

Given We are given that a person sells 32 oranges for a dollar to make a loss of 40%. We are asked to find the number of oranges he must sell in a dollar to make a profit of 20%

Approach We know that Selling Price = Cost Price *( 1 - Loss%) and Selling Price = Cost Price ( 1 + Profit%) Since we know the selling price and the loss%, we can find out the cost price.

Once we know the cost price and we know that the person needs to make a profit of 20%, we can find the selling price which would give us the number of oranges he needs to sell to make 20% profit.

Working Out The person sells 32 oranges in 1 dollar. So, his SP for 1 orange = \(\frac{1}{32}\). Since he has made a loss of 40%, we can write

SP = CP *(1 - 0.4) i.e. CP for one orange = \(\frac{1}{32* 0.6}\)

For the person to make 20% profit, he would need to have his SP = CP (1 + 0.2) = 1.2*CP. Since we know the CP of 1 orange, we can write

SP for one orange to make a profit of 20% = \(1.2 * \frac{1}{32*0.6}\) = \(\frac{1}{16}\) i.e. selling price of 1 orange to make a profit of 20% is \(\frac{1}{16}\) dollars. So he needs to sell 16 oranges for a dollar to make a profit of 20%.

In such questions avoid calculating numbers at each point as the numbers taken together will cancel out to give the final answer.

By selling 32 orange in a dollar, a man loses 40%. How many orange must he sell in a dollar to gain 20% profit?

A.16 B.18 C.20 D.25 E.28

Solution: simply use new quantity = 32* (100-60)/(100+20) = 16

I have the same logic as that of Brandon. Very elegantly solved by him!

I like Sagarsir's approach. Harsh' approach also works, but he accidentally made a mistake in his math. His formula works, but CP for one orange is 1/32 divided by .6 (not multiplied by .6). 1.2*1/32 divided by .6 will get to 1/16, as he says. But Like Sagarsir states, there are easier ways to solve this problem!
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By selling 32 orange in a dollar, a man loses 40%. How many orange must he sell in a dollar to gain 20% profit?

A.16 B.18 C.20 D.25 E.28

Solution: simply use new quantity = 32* (100-60)/(100+20) = 16

I have the same logic as that of Brandon. Very elegantly solved by him!

I like Sagarsir's approach. Harsh' approach also works, but he accidentally made a mistake in his math. His formula works, but CP for one orange is 1/32 divided by .6 (not multiplied by .6). 1.2*1/32 divided by .6 will get to 1/16, as he says. But Like Sagarsir states, there are easier ways to solve this problem!

Hi Brandon,

We are both saying the same thing . You are right to say that CP for one orange = \(\frac{SP}{0.6}\). Since SP for one orange = \(\frac{1}{32}\) that would give us CP = \(= \frac{1}{32} * \frac{1}{0.6}\) which is what I have mentioned in my solution

Re: By selling 32 orange in a dollar, a man loses 40%. How many orange [#permalink]

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20 Jul 2015, 08:48

Please let me know my approach is correct or wrong.

For 1 dollar i.e 100 cents , we are selling 32 oranges and getting a loss of 40%. So in order to get no loss or no profit, I need to sell 32 oranges at 140 cents. That means cost price of 32 oranges is 140 cents.

Now going by options, for example cost of price of 16 oranges is 70 cents, if I sell 16 oranges at 100 cents, I am likely to get 30% profit. That means if I sell 16 oranges, I mostly likes to get more than 20% profit. Likewise , I get the following profit percentages for the following options A) 16 oranges ~30% profit B) 18 oranges ~22% profit C) 20 oranges ~12% profit D) 25 oranges ~9% loss E) 28 oranges ~22% loss

This shows that option A i.e 16 orangs is sufficient to give us 20% profit.

Re: By selling 32 orange in a dollar, a man loses 40%. How many orange [#permalink]

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10 Jul 2016, 10:26

let c=cost of oranges per dollar p=selling price of oranges per dollar x=# of oranges he needs to sell per dollar to make 20% profit p/32=.6c p/x=1.2c .6c*32=1.2c*x x=16

Re: By selling 32 orange in a dollar, a man loses 40%. How many orange [#permalink]

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18 Oct 2017, 10:13

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