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

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Bunuel
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The cost price of 10 articles is equal to the selling price of 8 artic [#permalink] New post   26 Nov 2018, 02:13
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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%

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If 8 articles were sold at the cost price of 10 articles, find gain or loss percent.
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D
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Re: The cost price of 10 articles is equal to the selling price of 8 artic [#permalink] New post   26 Nov 2018, 02:20
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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%

Show Spoiler
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] New post   26 Nov 2018, 03:57
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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] New post   26 Nov 2018, 14:58
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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] New post   09 Dec 2018, 20:10
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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soapbolt
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Re: The cost price of 10 articles is equal to the selling price of 8 artic [#permalink] New post   09 Dec 2018, 20:18
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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Re: The cost price of 10 articles is equal to the selling price of 8 artic [#permalink] New post   09 Dec 2018, 20:38
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)
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Re: The cost price of 10 articles is equal to the selling price of 8 artic [#permalink] New post   02 Jan 2020, 11:47
C.P * 10 = S.P * 8

S.P = C.P *(10/8) = C.P *(5/4)

Hence fraction 5/4 is equivalent of 25% increase

So Gain of 25% is the answer
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Re: The cost price of 10 articles is equal to the selling price of 8 artic [#permalink] New post   04 Jan 2020, 20:17
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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%

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


We can create the equation:

10C = 8S

5C = 4S

If cost price = 4, then sale price = 5. Thus:

(5 - 4)/4 x 100 = 1/4 x 100 = 25% gain.

Answer: D
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Re: The cost price of 10 articles is equal to the selling price of 8 artic [#permalink] New post   05 Jan 2020, 01:25
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%

10 C = 8S = 80
10 C = 80 and 8 S = 80
C = 8 S = 10

Profit = (S-C/C)100
= 2/8*100
= 25%(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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