Profit And Loss
Math MCQs

Question :    A vendor buys 33 articles for $1 and sells 32 articles for $1. How much percent will he earn in this?

Correct Answer  3.13%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 33 articles = $1

The Sale Price (SP) for 32 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 33 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₃₃

∵ The Sale Price (SP) for 32 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₃₂

Calculation of profit

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

= ¹/₃₂ – ¹/₃₃

= ^{33 – 32}/₁₀₅₆

⇒ Profit = ¹/₁₀₅₆

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₃₃, the the profit = ¹/₁₀₅₆

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

= ^{1/₁₀₅₆}/_¹/33

= ¹/₁₀₅₆ × ³³/₁

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

= ¹/₁₀₅₆ × ³³/₁ × 100

= ^{1 × 33 × 100}/_{1056 × 1}

= ³³⁰⁰/₁₀₅₆ = 3.13

Thus, Profit = 3.13% 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 33 articles = $1

And, the Sale Price (SP) of 32 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 33 and 32 = 1056

Now, Let total number of articles purchased = 1056

Here, since the Cost Price of 33 articles = $1

∴ the Cost Price of 1 articles = ¹/₃₃

Therefore, the Cost Price of 1056 articles

And, since the Sale Price of 32 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₃₂

Therefore, the Sale Price of 1056 articles

= ¹/₃₂ × 1056 = $33

⇒ The Sale Price (SP) of 1056 articles = $33

Now, the Cost Price (CP) of 1056 articles = $32

And, the Sale Price (SP) of 1056 articles = $33

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)

= 33 – 32 = 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}/₃₂

= ¹⁰⁰/₃₂ = 3.13

Thus, profit = 3.13% Answer

Similar Questions

(1) A shopkeeper earns 130% after selling some old bikes for $5773. What was his cost price?

(2) Bill sold a bicycle for $840. If he purchased it at $600, then calculate his profit and profit percent in this sale.

(3) Find the earnings percentage if a vendor buys 52 articles for $1 and sells 51 articles for $1.

(4) 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.?

(5) Mr. Oliver loses 79% by selling an article for $800.10. For how much should he sell it to get a profit of 78%?

(6) Mr. Peter earns a profit of 110% by selling goods for $4431.00. For how much was he purchased those goods?

(7) By selling some goods for $3249 a shopkeeper earns a profit of 90%. Find the cost price of those goods.

(8) If a vendor bought 62 candies for $1 and sold 61 candies per $1 then find the profit percent.

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

(10) What is the cost price if Mrs. Norrah gets a profit of 165% by selling some items for $8506.5