Profit And Loss
Math MCQs

Question :    Find the earnings percentage if a vendor buys 52 articles for $1 and sells 51 articles for $1.

Correct Answer  1.96%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 52 articles = $1

The Sale Price (SP) for 51 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 52 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₅₂

∵ The Sale Price (SP) for 51 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₅₁

Calculation of profit

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

= ¹/₅₁ – ¹/₅₂

= ^{52 – 51}/₂₆₅₂

⇒ Profit = ¹/₂₆₅₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₅₂, the the profit = ¹/₂₆₅₂

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

= ^{1/₂₆₅₂}/_¹/52

= ¹/₂₆₅₂ × ⁵²/₁

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

= ¹/₂₆₅₂ × ⁵²/₁ × 100

= ^{1 × 52 × 100}/_{2652 × 1}

= ⁵²⁰⁰/₂₆₅₂ = 1.96

Thus, Profit = 1.96% 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 52 articles = $1

And, the Sale Price (SP) of 51 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 52 and 51 = 2652

Now, Let total number of articles purchased = 2652

Here, since the Cost Price of 52 articles = $1

∴ the Cost Price of 1 articles = ¹/₅₂

Therefore, the Cost Price of 2652 articles

And, since the Sale Price of 51 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₅₁

Therefore, the Sale Price of 2652 articles

= ¹/₅₁ × 2652 = $52

⇒ The Sale Price (SP) of 2652 articles = $52

Now, the Cost Price (CP) of 2652 articles = $51

And, the Sale Price (SP) of 2652 articles = $52

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)

= 52 – 51 = 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}/₅₁

= ¹⁰⁰/₅₁ = 1.96

Thus, profit = 1.96% Answer

Similar Questions

(1) A trader loses 47% by selling an article for $1171.30. For how much should he sell it to get a profit of 46%?

(2) Find the cost price, if Mrs. Julie earns a profit of 360% by selling some articles for $32706

(3) Mrs. Julie purchased 27 oranges for $1 and sold 26 oranges for $1. What will be his profit percentage?

(4) Mr. John buys 28 articles for $1 and sells 27 articles for $1 then, find his profit percent.

(5) Find the cost price, if a shopkeeper earns a profit of 80% by selling an article for $2718

(6) Find the cost price, if a trader gets a loss of 60% by selling five TV sets for $4724

(7) Mr. John earns a profit of 190% by selling a old car for $10759. For how much had he purchased that house?

(8) If a broker loses 39% by selling some of his stocks for $1104.10 then he should sell them for how much to get a profit of 38%?

(9) A car dealer earns 135% by selling an old antique car for $6133.50. For how much had he purchased that car?

(10) Find the profit percent if Mrs. Julie buys 29 bananas for $1 and sells 28 bananas for $1.