Profit And Loss
Math MCQs

Question :    Calculate the earnings in percent if a vendor buys 72 coins for $1 and sells 71 coins for $1.

Correct Answer  1.41%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 72 articles = $1

The Sale Price (SP) for 71 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 72 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₇₂

∵ The Sale Price (SP) for 71 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₇₁

Calculation of profit

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

= ¹/₇₁ – ¹/₇₂

= ^{72 – 71}/₅₁₁₂

⇒ Profit = ¹/₅₁₁₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₇₂, the the profit = ¹/₅₁₁₂

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

= ^{1/₅₁₁₂}/_¹/72

= ¹/₅₁₁₂ × ⁷²/₁

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

= ¹/₅₁₁₂ × ⁷²/₁ × 100

= ^{1 × 72 × 100}/_{5112 × 1}

= ⁷²⁰⁰/₅₁₁₂ = 1.41

Thus, Profit = 1.41% 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 72 articles = $1

And, the Sale Price (SP) of 71 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 72 and 71 = 5112

Now, Let total number of articles purchased = 5112

Here, since the Cost Price of 72 articles = $1

∴ the Cost Price of 1 articles = ¹/₇₂

Therefore, the Cost Price of 5112 articles

And, since the Sale Price of 71 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₇₁

Therefore, the Sale Price of 5112 articles

= ¹/₇₁ × 5112 = $72

⇒ The Sale Price (SP) of 5112 articles = $72

Now, the Cost Price (CP) of 5112 articles = $71

And, the Sale Price (SP) of 5112 articles = $72

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)

= 72 – 71 = 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}/₇₁

= ¹⁰⁰/₇₁ = 1.41

Thus, profit = 1.41% Answer

Similar Questions

(1) By selling an article for $15443.50, Mrs. Linda earns a profit of 235%. What was the cost price?

(2) Mr. Robert buys 31 articles for $1 and sells 30 articles for $1. Find the profit in percent.

(3) Find the cost price, if a trader gets a loss of 47% by selling 500 kg rice for $4881.30

(4) Mr. Bob gets a loss of 11% after selling an article for $364.90. For how much would he sell it to get a profit of 10%?

(5) A trader loses 54% by selling an article for $1177.60. For how much should he sell it to get a profit of 53%?

(6) Potter loses 91% by selling an article for $396.90. For how much should he sell it to get a profit of 90%?

(7) A shopkeeper earns a profit of 125% after selling some items for $5422.50. Find the cost price of those items.

(8) If a broker gets a loss of 22% by selling 100 shares for $3283.80, then find the cost price of those shares.

(9) After selling some items for $6884.50 Mr. Bob earns 145%. Find the cost price of those items.

(10) If a shopkeeper earns a profit of 5% by selling an article at $210, then find the cost price of that article.