Profit And Loss
Math MCQs

Question :    Find the profit percent if a vendor buys 9 articles for $1 and sells 8 articles for $1.

Correct Answer  12.5%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 9 articles = $1

The Sale Price (SP) for 8 articles = $1

Thus, Profit percent = ?

Unitary Method to find the profit when Cost Price and Sale Price are given

∵ The Cost Price (CP) for 9 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₉

∵ The Sale Price (SP) for 8 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₈

Calculation of profit

Profit = Sale Price (SP) – Cost Price (CP)

= ¹/₈ – ¹/₉

= ^{9 – 8}/₇₂

⇒ Profit = ¹/₇₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₉, the the profit = ¹/₇₂

∴ When the Cost Price (CP) is 1, then the profit

= ^1/₇₂/_¹/9

= ¹/₇₂ × ⁹/₁

∴ When the Cost Price (CP) is 100, then the profit

= ¹/₇₂ × ⁹/₁ × 100

= ^{1 × 9 × 100}/_{72 × 1}

= ⁹⁰⁰/₇₂ = 12.5

Thus, Profit = 12.5% Answer

Method (2) to find the profit%

Finding the profit percent by taking LCM of the number of articles purchased and sold for the same price

Given, the Cost Price (CP) of 9 articles = $1

And, the Sale Price (SP) of 8 articles = $1

Here, we need to take the LCM of number of articles purchased and sold to make them uniform.

Calculation of the Cost Price (CP) and the Sale Price

The LCM of 9 and 8 = 72

Now, Let total number of articles purchased = 72

Here, since the Cost Price of 9 articles = $1

∴ the Cost Price of 1 articles = ¹/₉

Therefore, the Cost Price of 72 articles

And, since the Sale Price of 8 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₈

Therefore, the Sale Price of 72 articles

= ¹/₈ × 72 = $9

⇒ The Sale Price (SP) of 72 articles = $9

Now, the Cost Price (CP) of 72 articles = $8

And, the Sale Price (SP) of 72 articles = $9

Calculation of the Profit, when the Cost Price (CP) and the Sale Price (SP) are given

Formula to find the profit when the Cost Price (CP) and the Sale Price (SP) are given

Profit = Sale Price (SP) – Cost Price (CP)

= 9 – 8 = 1

⇒ Profit = $1

Calculation of Profit percent using the formula

Formula to calculate the profit percent

Profit percent = ^{Profit × 100}/_{Cost Price}

Thus, profit % = ^{1 × 100}/₈

= ¹⁰⁰/₈ = 12.5

Thus, profit = 12.5% Answer

Similar Questions

(1) If a hawker bought 23 apples per $1 and sold them at a rate of 22 apples per $1, then what would his profit percent be?

(2) A shopkeeper earns a profit of 50% by selling an article for $1365. Find the cost price of the article.

(3) Mr. Bose loses 97% by selling an article for $141.30. For how much should he sell it to get a profit of 96%?

(4) A hawker buys 19 articles for $1 and sold then at the rate of 18 articles per $1. What was this profit percent?

(5) William loses 43% by selling an article for $1145.70. For how much should he sell it to get a profit of 42%?

(6) Find the cost price if Mr. Rocky earns a profit of 105% by selling an article for $4120.50

(7) James loses 67% by selling an article for $1059.30. For how much should he sell it to get a profit of 66%?

(8) Find the cost price, if Mr. Oliver earns a profit of 150% by selling an article for $7275.00

(9) Find the cost price, if a house broker earns a profit of 365% by selling a plot for $33526.5

(10) In an auction, Mr. Jojo got $27242.5 for his antique bike. If he got a profit of 325% in this deal, then what was his cost price.?