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# The cost price of 10 articles is equal to the selling price of 8 artic

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Math Expert
Joined: 02 Sep 2009
Posts: 51215
The cost price of 10 articles is equal to the selling price of 8 artic  [#permalink]

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26 Nov 2018, 01:13
00:00

Difficulty:

55% (hard)

Question Stats:

60% (00:34) correct 40% (00:53) wrong based on 53 sessions

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The cost price of 10 articles is equal to the selling price of 8 articles. The gain or loss percent is :

(A) Loss 25%
(B) Loss 20%
(C) Gain 20%
(D) Gain 25%
(E) Gain 30%

If 8 articles were sold at the cost price of 10 articles, find gain or loss percent.

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Re: The cost price of 10 articles is equal to the selling price of 8 artic  [#permalink]

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26 Nov 2018, 01:20
1
Bunuel wrote:
The cost price of 10 articles is equal to the selling price of 8 articles. The gain or loss percent is :

(A) Loss 25%
(B) Loss 20%
(C) Gain 20%
(D) Gain 25%
(E) Gain 30%

If 8 articles were sold at the cost price of 10 articles, find gain or loss percent.

Let the cost price per article be $$x$$
Let the selling price per article be $$y$$

Assume $$10x = 8y = 100$$
$$10x = 100$$
$$x = 10$$

$$8y = 100$$
$$y = 12.5$$

$$10 → 12.5$$
$$25$$% Gain

Hence, D.
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Re: The cost price of 10 articles is equal to the selling price of 8 artic  [#permalink]

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26 Nov 2018, 02:57
1
I solved in the following way

(10) C.P. = (8) S.P. .......(I)

or $$\frac{S.P}{C.P}$$ = $$\frac{10}{8}$$ ........(II)

clearly from 1 we have S.P. for 10 items will be more than C.P for 10 items hence there will be gain.

Gain % = $$\frac{(SP-CP)}{CP}$$ * 100

or = $$(\frac{SP}{CP} -1)$$ *100

from equation (II) we have

= $$(\frac{10}{8}-1)$$*100
= 25%

OPTION D is correct choice
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Re: The cost price of 10 articles is equal to the selling price of 8 artic  [#permalink]

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26 Nov 2018, 13:58
1
10 articles at price x = 8 articles at price y

10x=8y=100
x=10
y=12.5

Determine change
(new-old)/old
=(2.5/10) x (100)
=25%

*excuse my basic language on this
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Re: The cost price of 10 articles is equal to the selling price of 8 artic  [#permalink]

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09 Dec 2018, 19:10
Can you pls explain why it is equal to 100

"10x=8y=100"

sarajkluz wrote:
10 articles at price x = 8 articles at price y

10x=8y=100
x=10
y=12.5

Determine change
(new-old)/old
=(2.5/10) x (100)
=25%

*excuse my basic language on this

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Re: The cost price of 10 articles is equal to the selling price of 8 artic  [#permalink]

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09 Dec 2018, 19:18
sunita123 wrote:
Can you pls explain why it is equal to 100

"10x=8y=100"

He just assumed it randomly, it can be anything because we taking the ratio here and eventually all the extra thing will going to cancel out.

Suppose if we consider

10X= 8Y = 1000

then X = 100 and Y = 125
=> change will be
$$\frac{125-100}{100}$$ *100

= 25%

again the same result.

Hope it helped
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WTF is “that” doing in my sentence? By VerbalNinja

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Re: The cost price of 10 articles is equal to the selling price of 8 artic  [#permalink]

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09 Dec 2018, 19:38
CP of 10 articles = SP of 8 articles

Let's assume that CP of 10 articles = 100
Therefore, CP of 1 article will be = 10

SP of 8 articles = 100
SP of 1 article = 12.5

The key figures here to get to the answer are 12.5 and 10.

%increase = $$\frac{change}{original}$$$$*$$100 => $$\frac{2.5}{10}$$$$*$$100 => 2.5$$*$$10 =>25

D is the answer (25% gain)
Re: The cost price of 10 articles is equal to the selling price of 8 artic &nbs [#permalink] 09 Dec 2018, 19:38
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