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Ratio..

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Ratio.. [#permalink]

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New post 10 Feb 2011, 17:05
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I have big problems with this type of questions

A new released book includes hardback and paperback. If the sales price for the hardback is $20, and the sales price for the paperback is $15, what is the average price for all of the books sold during a certain day?
(1) The ratio of the number of the hardback sold to the number of paperback sold is 5 to 3.
(2) A total of 160 books were sold during the day.

or

129. On a certain date, Jack invested $13,000 at x percent simple annual interest and a different amount at у percent simple annual interest. If he earned same amount of interest from two investments, what amount did Jack invest at у percent simple annual interest?
(1) The amount of interest earned by Jack from the investment that pay x% interest was $390.
(2) The ratio of x to у is 3 to 2.




do you have some collection of these types of questions?...

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Re: Ratio.. [#permalink]

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New post 10 Feb 2011, 17:14
I think for the 1st prob C is right answer.

5:3 means 3 out of 8 was P and 5 out of 8 was H.

So x/160=3/8
x=P=60
Price of P = (60*15)
Same way we can get price of H and therefore the average.
Am I right?

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New post 10 Feb 2011, 17:19
The first answer is A... so I don't get, how we can solve it, if we don't know a total number...

The second answer must be B

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New post 11 Feb 2011, 03:16
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banksy wrote:
I have big problems with this type of questions

A new released book includes hardback and paperback. If the sales price for the hardback is $20, and the sales price for the paperback is $15, what is the average price for all of the books sold during a certain day?
(1) The ratio of the number of the hardback sold to the number of paperback sold is 5 to 3.
(2) A total of 160 books were sold during the day.


Let HB sold be 5x and PB sold be 3x.

Therefore, avg price = total price / total books
= 5x * 20 + 3x * 15 / 5x + 3x
= 145x/8x = a definite number.

Hence, only A is enough
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New post 11 Feb 2011, 09:19
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Samidh is correct.

With ratios you do not need to have the total number of books sold because the relationship established by the proportion will provide you with enough information to generate a solution.

Think of it like this: since the ratio of hardcovers to paperbacks is 5 to 3, you know that for every 5 hardcovers sold, you sell 3 paperbacks. 5 hardcovers @ $20 is $100 and 3 paperbacks @ $15 is $45. 8 books for $145 averages out to $18.125

Now do it with 10 hardcovers and 6 paperbacks (it's still a 5 to 3 ratio). 10 hardcovers @ $20 is $200 and 6 paperbacks @ $15 is $90. 16 books for $290 averages out to $18.125.

As you can see the number of books sold is irrelevant to the question as long as we have the ratio.

Hope that helps.

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New post 11 Feb 2011, 09:32
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As for the second one set it up like this:

x = rate on $13,000
P = principal with rate y
y = rate on P

Rate x applied to $13,000 generates the same amount of interest as rate y on unknown principal P implies the following equation:

13000x = Py

1 equation with 3 unknowns but you'll need at least 2 of the unknowns to solve.

Option 1 only tells you the left side of the equation, i.e. $390 = 13000x = Py

Option 2 gives you the ratio of rate x to rate y as 3 to 2. Just plug those numbers in for x and y and solve.

13000(3) = P(2)
39000 = 2P
19500 = P

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New post 12 Feb 2011, 05:38
On a certain date, Jack invested $13,000 at x percent simple annual interest and a different amount at у percent simple annual interest. If he earned same amount of interest from two investments, what amount did Jack invest at у percent simple annual interest?
(1) The amount of interest earned by Jack from the investment that pay x% interest was $390.
(2) The ratio of x to у is 3 to 2.


This is simple one:

a= the second amount invested

\(13000*x=a*y\)

\(13000*\frac{x}{y}=a\)

To find "a", you only have to know the ratio x to y, which is stated in (2)
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New post 21 Feb 2011, 04:28
I think for these kinds of Problems , We would have top 'pause' a bit before we choose the Ans. They have the compelling notion to let us go with ''C''.

Prob 1:

Ratio Problems - We would the Average Price per Book If we know the total costs and the total Number of books.

Average Price = Total Cost[fraction][/fraction] Total No:of Books = 20X + 15Y / X+Y

It is here we tend to make a mistake assuming that we need the total Information asked above.

But , I guess when a ration is given , its always either the same number like 5 Hard Back and 3 Paper Back or a Multiple of the above given Numbers.

So, the Equation would go - 20*5 + 15*3/5=3 or 20*10(Multiple of 5) + 15*6(Multiple of 3) / 10 +6

And we would get - 100 + 145 / 8 or 290 / 16 and so on ...

Either way the average price would be the same as Total amount and the Total No: of Books do Increase Proportionally.

But then If We had a Question that Asked - What is the Exact Total Amount collected due to the sale of the both kinds - Then we would have a ONE single Answer, We would need more variable to solve.

Prob : 2

If he earned same amount of interest from two investments,

The above line is what is most Important for we would know that reagardless of X or Y % the Interest earned from both principles is the same.

From Statement 1 , X = $390 or 3%Interest.

Let's see If we can deduce the Y , Now Y = $ 390,
If $390 is a 1% Interest than the Principle would be = $100 * $390 = $39000,

and if it is 2% then we have = $50 * $390= $19500. So we have more than two Answers = Not Sufficient.

From Statement 2 : Interest Ratio for X: Y is 3:2

Assume X= 3% (or any Multiple of 3) , We get $1300*3/100 = $390 ,

Now we know that from the starement mentioned above that the Interest Amount for both the PRINCIPLES is the SAME.
So since $390 is 3% of $13,000, $390 would be 2% of =$ 390*$50 = $ 19500

You can even take the Interest X as 6 % and Y as 4 % and so on, We can arrive at the same Principle

Hope that Helps !

Best.

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New post 21 Feb 2011, 19:09
The first one is A, as we don't need to know the total revenues. Second one is b.

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Re: Ratio..   [#permalink] 29 Mar 2017, 02:19
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