Aptitude Discussion

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 |

**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 1/4^{th} 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.**

**Sikandar Naeem**

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**Yogesh**

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cp*5/4=1000

cp=800---------A

1000*125/100=1250

1250-1000=250--B

B-A=50

**Nimesh Goyal**

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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**

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$125\%$ 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 $= 50$

Merchant A - 200

Merchant B - 250

For Merchant A: (Computes Profit on cost)

selling price = Cost + Profit (25% of cost)

Selling Price = 125 % Cost

1000 RS = 125% cost

cost = 1000/125% => 800 RS

For Merchant B (Computes Profit on Selling price)

Selling Price = Cost + Profit (25% of Selling Price)

Cost = selling price - profit (25% of Selling Price)

cost = 1000- (1000 * 25%)

cost = 750 Rs

Difference in cost of both Merchants

Merchant A - Merchant B

= 800-750

= 50 Rs

As sales price of both Merchants is same therefore by saving cost by 50 Rs. Merchant B have more profit than Merchant A.