# Moderate Percentages Solved QuestionAptitude Discussion

 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

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.