Profit And Loss
Math MCQs

Question :    If Mr. Steve buys 41 articles for $1 and sells 40 articles for $1 then find the profit percent.

Correct Answer  2.5%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 41 articles = $1

The Sale Price (SP) for 40 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 41 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₄₁

∵ The Sale Price (SP) for 40 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₄₀

Calculation of profit

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

= ¹/₄₀ – ¹/₄₁

= ^{41 – 40}/₁₆₄₀

⇒ Profit = ¹/₁₆₄₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₄₁, the the profit = ¹/₁₆₄₀

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

= ^{1/₁₆₄₀}/_¹/41

= ¹/₁₆₄₀ × ⁴¹/₁

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

= ¹/₁₆₄₀ × ⁴¹/₁ × 100

= ^{1 × 41 × 100}/_{1640 × 1}

= ⁴¹⁰⁰/₁₆₄₀ = 2.5

Thus, Profit = 2.5% 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 41 articles = $1

And, the Sale Price (SP) of 40 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 41 and 40 = 1640

Now, Let total number of articles purchased = 1640

Here, since the Cost Price of 41 articles = $1

∴ the Cost Price of 1 articles = ¹/₄₁

Therefore, the Cost Price of 1640 articles

And, since the Sale Price of 40 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₄₀

Therefore, the Sale Price of 1640 articles

= ¹/₄₀ × 1640 = $41

⇒ The Sale Price (SP) of 1640 articles = $41

Now, the Cost Price (CP) of 1640 articles = $40

And, the Sale Price (SP) of 1640 articles = $41

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)

= 41 – 40 = 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}/₄₀

= ¹⁰⁰/₄₀ = 2.5

Thus, profit = 2.5% Answer

Similar Questions

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(2) Find the cost price, if a trader gets a loss of 50% by selling 500 bags of rice for $4905

(3) If a shopkeeper gets a loss of 65% by selling five TV sets for $4483.50 then find the cost price of all those TV sets.

(4) Potter loses 89% by selling an article for $474.10. For how much should he sell it to get a profit of 88%?

(5) Mr. Steven loses 93% by selling an article for $315.70. For how much should he sell it to get a profit of 92%?

(6) If a dealer loses 61% by selling an article for $1134.90. For how much should he sell it to get a profit of 60%?

(7) By selling a house for $14332.50, a dealer earns a profit of 225%. Find the cost price

(8) By selling some items for $1788.90 a vendor gets a loss of 11%. Find the cost price of those items.

(9) A shopkeeper loses 51% by selling an article for $1180.90. For how much should he sell it to get a profit of 50%?

(10) A trader loses 53% by selling an article for $1179.70. For how much should he sell it to get a profit of 52%?