apples problem

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sohailmbaprep: Senior | Next Rank: 100 Posts; Posts: 59; Joined: Thu Feb 23, 2012 11:18 pm

by sohailmbaprep » Wed Oct 17, 2012 3:08 am

Mr X buys some apples at 5 per rupee from one trader ,and a similar quantity at 7 per rupee from another trader.He mixes both the varieties, and sells the whole at 6 per rupee.What is the profit or loss % that he makes ?

is it a mixture problem ?? how can i solve this

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Source: Beat The GMAT — Problem Solving | Wed Oct 17, 2012 3:08 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Oct 17, 2012 6:10 am

sohailmbaprep wrote:Mr X buys some apples at 5 per rupee from one trader ,and a similar quantity at 7 per rupee from another trader.He mixes both the varieties, and sells the whole at 6 per rupee.What is the profit or loss % that he makes ?

is it a mixture problem ?? how can i solve this

Mr X buys some apples at 5 per rupee from one trader.
Let's say that he buys x apples.
This means his cost will be x/5 rupee

Mr X buys a similar quantity at 7 per rupee
I'm assuming that "similar" means "equal" here.
So, he buys x apples
This means his cost will be x/7 rupee

So, his total cost is x/5 + x/7 rupee
Let's combine the fractions to get a total cost of 12x/35 rupee

Mr X sells the whole at 6 per rupee.
He has 2x apples
At 6 per rupee, he will make 2x/6 rupee

Expense = 12x/35 rupee
Revenue = 2x/6 rupee

To compare these, we'll need to write them with a common denominator of 210 to get:
Expense = 72x/210 rupee
Revenue = 70x/210 rupee

As you can see, Mr. X loses money.
To calculate the % loss, we calculate (100)(72-70)/72
We get about 2 56/72% or about 2.8%

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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subhakam: Senior | Next Rank: 100 Posts; Posts: 38; Joined: Mon Jun 21, 2010 12:37 pm

by subhakam » Fri Dec 14, 2012 1:56 pm

Hi Brent - the below does not make sense to me - help I am confused. (when i pick smart numbers)
Let us take your case - RS 5 be Brand A (apples)
For Brand A - total quantity is say 10 apples. Therefore total cost = Rs 50

Brand B : Rs 7 per apple. Since the question states similar quantity, let us say 10 apples of Brand B were purchased as well
For Brand B - Total quantity = 10 and total price/cost= Rs 7 X 10 = Rs 70

Now Total Amount spent for both brands = 50 + 70 = 120 and Total Quantity is 20 apples.

If the person sells them for Rs 6 each - then total amount of revenue = 16 X 20 = RS 120

It breaks even - so to me there is no profit or loss.

Please advise
Thanks
Subhakam

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puneetkhurana2000: Master | Next Rank: 500 Posts; Posts: 131; Joined: Wed Nov 14, 2012 2:01 pmFollowed by: 2 members; Thanked: 39 times

by puneetkhurana2000 » Fri Dec 14, 2012 2:21 pm

Hi Subhakam, 5 and 7 are apples which can be bought for a rupee and not the prices per apple.

Similarly 6 apples can be sold for a rupee and it is not that an apple costs rupees 6.

Hope this makes sense!!!

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Dec 14, 2012 3:03 pm

sohailmbaprep wrote:Mr X buys some apples at 5 per rupee from one trader ,and a similar quantity at 7 per rupee from another trader.He mixes both the varieties, and sells the whole at 6 per rupee.What is the profit or loss % that he makes ?

is it a mixture problem ?? how can i solve this

Let the number of apples purchased from each trader = the LCM of 5, 6 and 7 = 210.

Trader one:
At 5 apples per rupee, the cost of 210 apples = 210/5 = 42 rupees.

Trader two:
At 7 apples per rupee, the cost of 210 apples = 210/7 = 30 rupees.

Total number of apples = 210+210 = 420.
Total cost = 42+30 = 72.

Revenue:
Since 6 apples earn 1 rupee, the revenue for 420 apples = 420/6 = 70 rupees.

Loss = cost - revenue = 72-70 = 2.
Percent loss = loss/cost * 100 = 2/72 * 100 = 2.77%.

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