percentage issues

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percentage issues

by GmatTakerNo.1 » Sun Apr 25, 2010 1:30 pm
Hey,

have some problem to solve these questions. Please help me out.

1. Mr. Johnson invested $50,000 into two investments. Part of it he put in a gold mine stock from which he hoped to receive a 20% return per year. The rest he invested in a bank stock which was paying 6 percent per year. If he received $400 more the first year from the bank stock than from the mining stock, how much did he invest in each stock?

Answer: Gold 10000, bank 40000

2. Bob bought a goat. He expected to sell it at a price that would give him a 10% profit on his purchase. However, he had to sell it for $50 less than he expected, which was a loss of 15% on what it cost him. What did Bob pay for the goat?

Answer: 200 $

3. A room contains 160 people, 15% of whom are women. A group of people, 30% of whom are women, leaves the room. Of the people remaining in the room, 10% are women. How many people left the room?
a) 10
b) 20
c) 40
d) 80
e) 120

Answer D

4. John is able to buy 5 more apples for $1.00 when the price per apple decreases 20%. What was the original price of an apple?

Answer: 5 cents

5. A retailer sells cameras at a profit of 10%. If he had paid 10% less for it and sold it for $10 more, he would have made a profit of 25%. How much did it cost him and how much did he sell it for?

Answer: cp=400, sp= 440

6. A trader discovers that he can buy goods 10% cheaper if he gets them directly from the manufacturer. However, the cost of transportation increases by $100 per trip. If he makes a total savings of $250 per trip, what is the cost he pays to the manufacturer?

Answer: 3150 $

7. The interest compounded annually on a certain sum of money is $41.60 after two years. The simple interest on the same amount of money after two years would be $40.00. Find the amount invested if the interest rate would be the same in each investment.

Answer 250$


Thank you in advance.
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by akhpad » Mon Apr 26, 2010 12:56 am
Please post one problem in one post.

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by GmatTakerNo.1 » Mon Apr 26, 2010 2:20 am
Yeah, I´ll do in the next ones. I just did it because I donßt wanna lose the overview.

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by blaster » Mon Apr 26, 2010 2:22 am
GmatTakerNo.1 wrote:Hey,

have some problem to solve these questions. Please help me out.

1. Mr. Johnson invested $50,000 into two investments. Part of it he put in a gold mine stock from which he hoped to receive a 20% return per year. The rest he invested in a bank stock which was paying 6 percent per year. If he received $400 more the first year from the bank stock than from the mining stock, how much did he invest in each stock?

Answer: Gold 10000, bank 40000


Thank you in advance.
(50000-x)*20/100+400=x*6/100

solving this equation you get a right answer.

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by GmatTakerNo.1 » Mon Apr 26, 2010 2:51 am
Thanks for the solution of question one. I got it. Actually not that difficult ;)

Six questions left.

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by blaster » Mon Apr 26, 2010 3:41 am
GmatTakerNo.1 wrote:Hey,


2. Bob bought a goat. He expected to sell it at a price that would give him a 10% profit on his purchase. However, he had to sell it for $50 less than he expected, which was a loss of 15% on what it cost him. What did Bob pay for the goat?

Answer: 200 $



Thank you in advance.
the equation looks like this

x+x*10/100-50$=x-x*15/100


P.S. the logic all this question is almost similar. hope it helps

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by Nilakshi1001 » Mon Apr 26, 2010 4:41 am
Answer to question number 3 should be 40.

C

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by harshavardhanc » Mon Apr 26, 2010 5:29 am
GmatTakerNo.1 wrote:
2. Bob bought a goat. He expected to sell it at a price that would give him a 10% profit on his purchase. However, he had to sell it for $50 less than he expected, which was a loss of 15% on what it cost him. What did Bob pay for the goat?

See that a difference of 25% ( +10% - (-15%) ) is equal to $50. Hence, 100% will be 4 times 50 i.e $200.



3. A room contains 160 people, 15% of whom are women. A group of people, 30% of whom are women, leaves the room. Of the people remaining in the room, 10% are women. How many people left the room?
a) 10
b) 20
c) 40
d) 80
e) 120
Answer D


the answer here should be C=40 ppl left the room. Please re-check.

Method: consider this as a mixture problem, where you mix a 30% solution with a 5% solution, to get a 15% solution. Solution in our case would be women. You have to find in what ratio are they mixed.

30x + 5y = 15(x+y)
this gives, x:y = 3:1 or 3t: t

this means, the number of ppl who left the room is 1/3rd of the number of ppl left in the room.

ie. 4t = 160 or t = 40 (ANS)



4. John is able to buy 5 more apples for $1.00 when the price per apple decreases 20%. What was the original price of an apple?

If product of A and B is constant, i.s A * B = constant, a 20% decrease in one variable means a 25 % increase in the other one.

Here, Price * no. of apples is constant ($1). Therefore, a 20 % decrease in price would mean a 25 % increase in no. of apples purchased, which is given to be 5. Hence, 100% apples would be 4 times 5 = 20.

Answer, price / apple would be 100/20 = 5 cents


Answer: 5 cents

5. A retailer sells cameras at a profit of 10%. If he had paid 10% less for it and sold it for $10 more, he would have made a profit of 25%. How much did it cost him and how much did he sell it for?

first info says that : sp/cp = 11/10 . The second sentence says : (10+sp)/.9cp = 5/4

or 50/44 = (10+sp)/.9sp => 45sp = 440 + 44sp
or sp = 440 and cp = (10/11) * 440 = 400



Regards,
Harsha

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by GmatTakerNo.1 » Mon Apr 26, 2010 6:33 am
Hey, thanks for your answers.

The problem I have with question 2 is that why do I have to consider the 10 % of profit?
I mean the question says that he make a loss of 50 which is in my opinion the costs for the goat - 15% (50$).
hen you calculate from the selling price (1.1x), the first 10 % down to 1.0 is NOT a loss, isn´t it?

A loss is all what is under the price that he paid for the goat.

Am I wrong? I´m a little bit confused.


And yes, for question 3. the answer is C, sorry. ;)

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by kevincanspain » Mon Apr 26, 2010 6:58 am
he had to sell it for $50 less than he expected, which was a loss of 15% on what it cost him


The wording, while not ideal, makes it clear that, if he expected to sell Billy for 1.1c, he actually sold the goat for 0.85c
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by GmatTakerNo.1 » Mon Apr 26, 2010 8:59 am
Ok, so "expected" is the basis. Good to know for future Gmat questions.

Thanks guys. Good work.

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by clock60 » Mon Apr 26, 2010 12:47 pm
6. A trader discovers that he can buy goods 10% cheaper if he gets them directly from the manufacturer. However, the cost of transportation increases by $100 per trip. If he makes a total savings of $250 per trip, what is the cost he pays to the manufacturer?

Answer: 3150 $
i have problems with this one as my answer does not coincide with oa
the initial cost=x
the cost from manufacture=0,9x
x-(0,9x+100)=250
x=1500, and 0,9x=1350, but not 3150
it is a typo, or i am thinking wrong?

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by harshavardhanc » Mon Apr 26, 2010 2:02 pm
clock60 wrote:6. A trader discovers that he can buy goods 10% cheaper if he gets them directly from the manufacturer. However, the cost of transportation increases by $100 per trip. If he makes a total savings of $250 per trip, what is the cost he pays to the manufacturer?

Answer: 3150 $
i have problems with this one as my answer does not coincide with oa
the initial cost=x
the cost from manufacture=0,9x
x-(0,9x+100)=250
x=1500, and 0,9x=1350, but not 3150
it is a typo, or i am thinking wrong?
see it this way. The savings would actually be .1*x- 100, which is given to be $250.

Hence, .1x - 100 = 250 => .1*x = 350

the amount he pays to the manufacturer is .9x or 9 times 350 = $3150.

HTH.
Regards,
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by clock60 » Tue Apr 27, 2010 11:21 am
harshavardhanc wrote:
clock60 wrote:6. A trader discovers that he can buy goods 10% cheaper if he gets them directly from the manufacturer. However, the cost of transportation increases by $100 per trip. If he makes a total savings of $250 per trip, what is the cost he pays to the manufacturer?

Answer: 3150 $
i have problems with this one as my answer does not coincide with oa
the initial cost=x
the cost from manufacture=0,9x
x-(0,9x+100)=250
x=1500, and 0,9x=1350, but not 3150
it is a typo, or i am thinking wrong?
see it this way. The savings would actually be .1*x- 100, which is given to be $250.

Hence, .1x - 100 = 250 => .1*x = 350

the amount he pays to the manufacturer is .9x or 9 times 350 = $3150.

HTH.
thank you friend for your reply
but now i see that my solution is exactly the same as yours
but i commit math mistake when i did not change sign opening the brackets, so got wrong result