Percentages
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Q.

If the cost price of 20 articles is equal to the selling price of 16 articles, What is the percentage of profit or loss that the merchant makes?

 A.

$20\%$ Profit

 B.

$25\%$ Loss

 C.

$25\%$ Profit

 D.

$33.33\%$ loss

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Solution:
Option(C) is correct

Let Cost price of 1 article be Re.1.

Therefore, Cost price of 20 articles = Rs. 20.

Selling price of 16 articles = Rs. 20

Therefore, Selling price of 20 articles

\(=\dfrac{20}{16}\times 20\)

\(=25\)

Profit = Selling price - Cost price

$=25−20=5$

\(\text{Percentage of profit}=\dfrac{\text{profit}}{\text{C.P}}\times 100\)

\(=\dfrac{5}{20}\times 100\)

= 25% Profit

Edit: For an alternative solution, check comment by Uppendra.

Edit 2: For formula based yet another alternative solution, check comment by Chirag Goyal.

Edit 3: For yet another alternative solution, check comment by Sathish Kumar B.


(7) Comment(s)


Syed
 ()

20-16/16*100 =25% profit as we knew 20 considered sale price of 16 items and cost is 16 so simple formula will be use S.P-C.P/C.P*100=Profit percentage.



Param
 ()

Simplest One :

CP(20) = SP (16) ; CP of 20 articles is equal to SP of 16 articles (given)

Let CP of 1 Article be 1rs. CP of 20 article be 20rs.

CP(20) = 20rs = SP(16)

so above, SP(16) = 20rs

CP(16) = 16rs

Articles are same on cost & selling side. Find the profit or loss.

(20-16)/16*100 = 25% Profit.



Sathish Kumar B
 ()

let CP of 1 article be 100 and SP be $x$

Then,

$20 * 100 = 16 * x$

$20 * 100/16 = x$

$x = 125$

$\text{Profit} = sp - cp$

$= 125-100 = 25$

$ \text{Profit Percent}= \dfrac{25}{100} \times 100$

$= 25\%$



Chirag Goyal
 ()

$$\text{Profit percentage} = \left(\dfrac{\text{SP of 1 apple}}{\text{CP of 1 apple}} - 1\right)100$$



Uppendra
 ()

Given,

$20CP=16SP$

$CP=\dfrac{16}{20}SP$

$\dfrac{CP}{SP}=\dfrac{4}{5}$

$CP:SP=4:5$

Hence, $SP$ is greater.

Profit,

$\text{Profit %}=\dfrac{SP-CP}{CP}*100

$=\dfrac{5-4}{4}*100$

$=\textbf{25%}$



PRATYUSH ANAND
 ()

sorry my mistake profit is 25%.



PRATYUSH ANAND
 ()

Hi 2 all,

Given:-

CP of 20 Articles=SP of 16 Articles

Therefore,

CP of 1 Article= SP of 0.8 Article

Profit % formula $= \left(\dfrac{SP-CP}{CP}\right)\times 100

i.e $\Rightarrow \left(\dfrac{SP-0.8SP}{0.8SP}\right)\times 100=20\%$

Hence, $\textbf{20%}$ of profit.