Profit And Loss
Math MCQs

Question :    Find the earnings percentage if a vendor buys 53 articles for $1 and sells 52 articles for $1.

Correct Answer  1.92%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 53 articles = $1

The Sale Price (SP) for 52 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 53 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₅₃

∵ The Sale Price (SP) for 52 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₅₂

Calculation of profit

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

= ¹/₅₂ – ¹/₅₃

= ^{53 – 52}/₂₇₅₆

⇒ Profit = ¹/₂₇₅₆

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₅₃, the the profit = ¹/₂₇₅₆

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

= ^{1/₂₇₅₆}/_¹/53

= ¹/₂₇₅₆ × ⁵³/₁

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

= ¹/₂₇₅₆ × ⁵³/₁ × 100

= ^{1 × 53 × 100}/_{2756 × 1}

= ⁵³⁰⁰/₂₇₅₆ = 1.92

Thus, Profit = 1.92% 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 53 articles = $1

And, the Sale Price (SP) of 52 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 53 and 52 = 2756

Now, Let total number of articles purchased = 2756

Here, since the Cost Price of 53 articles = $1

∴ the Cost Price of 1 articles = ¹/₅₃

Therefore, the Cost Price of 2756 articles

And, since the Sale Price of 52 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₅₂

Therefore, the Sale Price of 2756 articles

= ¹/₅₂ × 2756 = $53

⇒ The Sale Price (SP) of 2756 articles = $53

Now, the Cost Price (CP) of 2756 articles = $52

And, the Sale Price (SP) of 2756 articles = $53

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)

= 53 – 52 = 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}/₅₂

= ¹⁰⁰/₅₂ = 1.92

Thus, profit = 1.92% Answer

Similar Questions

(1) Find the cost price, if a trader gets a loss of 74% by selling 50 bags of rice for $3798.60

(2) Mr. Robert sold his motorcycle for $1629 and got a loss of 10%. What was his cost price?

(3) William loses 71% by selling an article for $988.90. For how much should he sell it to get a profit of 70%?

(4) If a trader gets a loss of 14% by selling some articles for $2244.60 then what was his cost price?

(5) If a dealer earns a profit of 260% by selling an article for $18396.00. Find the cost price.

(6) A trader earns a profit of 100% by selling an article for $3820.00. Find the cost price.

(7) John purchased a bike for $500 and he sold it at a gain of 12%. Find the sale price of the bike.

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

(9) A dealer sold an antique piece of a car $25771.50. If he earns a profit of 315%, then find his cost price.

(10) Find the cost price, if a fruit seller gets a loss of 43% by selling 500 bags of fruits for $4793.70