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) If a vendor gets a loss of 21% by selling some apples for $3167.90 then what was the cost price of those apples?

(2) In a deal, Mr. Kart earns a profit of 85%. He got a total of $2978.50 in the deal. What was the cost price of this deal?

(3) Find the cost price, if a trader gets a loss of 63% by selling 15 TV sets for $4591.7

(4) William loses 69% by selling an article for $1026.10. For how much should he sell it to get a profit of 68%?

(5) Calculate the cost price, if a trader gets a loss of 3% by selling an article for $397.70

(6) Find the cost price, if a share broker gets a loss of 27% by selling 200 shares for $3803.30.

(7) After selling some antique items for $6504 a trader earns a profit of 140%. Find the cost price of those antique items.

(8) A broker earns a profit of 310% by selling a house for $25051. Find the cost price.

(9) On a closing day, a shopkeeper earns a profit of 65%. If gets $1996.5 in total, then what was his cost price?

(10) John loses 64% by selling an article for $1101.60. For how much should he sell it to get a profit of 63%?