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A person purchased a pen and a pencil for 15$

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tanu11
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A person purchased a pen and a pencil for 15$ [#permalink] New post   02 Oct 2020, 05:25
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A person purchased a pen and a pencil for 15$. He sold the pen at a 20% profit and the pencil at a 30% profit . if his total profit was 24%, find the cost price of the pen ?
A. 10.50
B. 9.5
C. 11
D. 10
E. 9
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E
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Re: A person purchased a pen and a pencil for 15$ [#permalink] New post   02 Oct 2020, 09:13
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This is just a weighted average problem. We have profits of 20% and 30% on two things, with a 24% profit overall. Using alligation, on a number line we have:

--20-----24-----------30--

and the ratio of the distances to the middle number is 4 to 6, so the ratio of the original prices of the pencil and pen must be 4 to 6 (the pen is the more expensive item, since 24 is closer to 20). So the pen cost 6/10 of the total of $15, or $9.
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CrackverbalGMAT
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Re: A person purchased a pen and a pencil for 15$ [#permalink] New post   02 Oct 2020, 05:42
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tanu11 wrote:
A person purchased a pen and a pencil for 15$. He sold the pen at a 20% profit and the pencil at a 30% profit . if his total profit was 24%, find the cost price of the pen ?
A. 10.50
B. 9.5
C. 11
D. 10
E. 9


Given that the Total CP = 15

Let the CP of the pen = x

Therefore, CP of the pencil = 15 - x


SP of the pen after a 20% Profit = x * 120/100 = 1.2x

SP of the pencil after a 30% Profit = (15 - x) * 130/100 = 19.5 - 1.3x


Total SP = 1.2x + 19.5 - 1.3x = 19.5 - 0.1x


We are given that he earned a total of 24% Profit on the transaction

Profit = SP - CP = 19.5 - 0.1x - 15 = 4.5 - 0.1x


Profit % = \(24 = \frac{Profit}{CP} * 100 = \frac{4.5 - 0.1x}{15} * 100\)

24 * 15 = (4.5 - 0.1x) * 100

360 = 450 - 10x

10x = 450 - 360 = 90

x = 9


Option E

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Re: A person purchased a pen and a pencil for 15$ [#permalink] New post   03 Oct 2020, 05:17
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I did it using a different method:

20%. 30%
\ /
24%
/ \
6 : 4
Therefore cost of pen=3/5 of original cost 15 ie 9 - option E

Posted from my mobile device
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Re: A person purchased a pen and a pencil for 15$ [#permalink] New post   03 Oct 2020, 08:26
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Cheaper(Pen) = 20% and Dearer(Pencil) = 30%.

Overall: 24%

Rule of Alligation: 24 - 20 = 4 and 30 - 24 = 6

Ratio = Pen : Pencil = 6 : 4 or 3 : 2

Pen cost: \(\frac{3 }{ 5}\) * 15 = 9

Answer E
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Re: A person purchased a pen and a pencil for 15$ [#permalink] New post   05 Oct 2020, 07:46
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tanu11 wrote:
A person purchased a pen and a pencil for 15$. He sold the pen at a 20% profit and the pencil at a 30% profit . if his total profit was 24%, find the cost price of the pen ?
A. 10.50
B. 9.5
C. 11
D. 10
E. 9

Solution:

Let’s let x = the cost of the pen and so (15 - x) = the cost of the pencil. The total price that he sold the pen for, which includes the profit, was 1.2x, and the total price that he sold the pencil for, including profit, was 1.3(15 - x). The total profit on the original $15 cost was 24%, so he sold the pair of items for 1.24 x 15. We can set up the equation:

1.2x + 1.3 (15 - x) = 1.24 x 15

1.2x + 19.5 - 1.3x = 18.60

0.9 = 0.1x

9 = x

The original cost of the pen was $9.

Answer: E
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A person purchased a pen and a pencil for 15$ [#permalink] New post   20 Oct 2020, 08:02
This is a weighted average problem. Since 24% is closer to 20%, the pen costs more than the pencil (more heavily weighted).

Answer is 9.
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Re: A person purchased a pen and a pencil for 15$ [#permalink] New post   20 Oct 2020, 22:23
Can use a Weighted Average Concept to solve the Cost Price of the Pen:

Data Point 1 - 30% Profit on Pencil

Weight of 1 - $Cost Price of Pencil = b


Data Point 2 - 20% Profit on Pen

Weight of 1 - $Cost Price of Pen = a


a + b = $15


the 24% NET Profit is closer to the 20% Profit on the PEN

Using the See-Saw scale

Pencil 30% --------------------------------24% Net Profit --------------------Pen 20%

Total Distance = 30% - 20% = 10

Relative Weighting of Pen = 30% - 24$ = 6

(6/10) of the Total Cost Price of (a + b = $15) is attributable to the Pen


(6/10) * $15 = Cost Price of Pen = $9

-E-
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Re: A person purchased a pen and a pencil for 15$ [#permalink] New post   09 Oct 2023, 07:08
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Re: A person purchased a pen and a pencil for 15$ [#permalink]
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