Percentages
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Q.

Two merchants sell, each an article for Rs.1000. If Merchant $A$ computes his profit on cost price, while Merchant $B$ computes his profit on selling price, they end up making profits of 25% respectively.

By how much is the profit made by Merchant $B$ greater than that of Merchant $A$? 

 A.

Rs.50.00

 B.

Rs.66.67

 C.

Rs.75.00

 D.

Rs.150.00

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Solution:
Option(A) is correct

Merchant $B$ computes his profit as a percentage of selling price. He makes a profit of 25% on selling price of Rs.1000. i.e. his profit $= 25/% \text{ of } 1000 = \text{Rs. }250$

Merchant $A$ computes his profit as a percentage of cost price.

If he makes a profit of 25% or 1/4th of his cost price, then his profit expressed as a percentage of selling price,

$=\dfrac{1}{1+4} = \left(\dfrac{1}{5}\right)^{th}$ or 20% of selling price.

So, Merchant $A$ makes a profit of $20\% \text{ of Rs. }1000 = \text{Rs. }200$

Hence, Merchant $B$ makes $\textbf{Rs.50}$ more profit than Merchant $A$.

Edit: For an alternative solution, check comment by Zoha Amjad.


(3) Comment(s)


Nimesh Goyal
 ()

CP + Profit = SP

4 + 1 = 5 { 25% in fraction is equal to 1/4. 1 represents profit over 4 CP}

5 + 1 =4 { 1 represents profit over 4 SP }

Since SP is equal to Rs. 1000

multiply first case by 200 and second case by 250.

The difference between profit will be equal to Rs.50



Zoha Amjad
 ()

$125\%$ of cost price $= 1000$

C.P. $= 800$

Profit $= 1000-800=200$

MERCHANT $A$,

$= \left(\dfrac{200}{800})\times 1000\right)$

$= 250$

MERCHANT $B$,

$= \left(\dfrac{200}{1000}\right)\times 1000$

$=200$

Difference $= 50$


Vejayanantham TR
 ()

Merchant A - 200

Merchant B - 250