Profit And Loss
Math MCQs

Question :    How much percent will Peter earn if he buys 37 articles for $1 and sells 36 articles for $1?

Correct Answer  2.78%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 37 articles = $1

The Sale Price (SP) for 36 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 37 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₃₇

∵ The Sale Price (SP) for 36 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₃₆

Calculation of profit

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

= ¹/₃₆ – ¹/₃₇

= ^{37 – 36}/₁₃₃₂

⇒ Profit = ¹/₁₃₃₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₃₇, the the profit = ¹/₁₃₃₂

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

= ^{1/₁₃₃₂}/_¹/37

= ¹/₁₃₃₂ × ³⁷/₁

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

= ¹/₁₃₃₂ × ³⁷/₁ × 100

= ^{1 × 37 × 100}/_{1332 × 1}

= ³⁷⁰⁰/₁₃₃₂ = 2.78

Thus, Profit = 2.78% 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 37 articles = $1

And, the Sale Price (SP) of 36 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 37 and 36 = 1332

Now, Let total number of articles purchased = 1332

Here, since the Cost Price of 37 articles = $1

∴ the Cost Price of 1 articles = ¹/₃₇

Therefore, the Cost Price of 1332 articles

And, since the Sale Price of 36 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₃₆

Therefore, the Sale Price of 1332 articles

= ¹/₃₆ × 1332 = $37

⇒ The Sale Price (SP) of 1332 articles = $37

Now, the Cost Price (CP) of 1332 articles = $36

And, the Sale Price (SP) of 1332 articles = $37

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)

= 37 – 36 = 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}/₃₆

= ¹⁰⁰/₃₆ = 2.78

Thus, profit = 2.78% Answer

Similar Questions

(1) Find the cost price, if a trader gets a loss of 67% by selling ten bags of apple for $4359.30

(2) A shopkeeper earns a profit of 175% by selling some antique articles for $9377.50. What was the cost price of those antique articles?

(3) Find the earnings percentage if a hawker buys 50 articles for $1 and sells 49 articles for $1.

(4) If John buys 68 pencils for $1 and sells them at a rate of 67 per $1 then calculate the profit percent in this selling.

(5) If Noah buys 32 articles for $1 and sells them at a rate of 31 articles per $1 then, find his profit percent.

(6) For how much should Mr. John sell it to get a profit of 3% if he loses 4% by selling an article for $57.60?

(7) If a trader earned a profit of 350% by selling a housing plot for $31095 then, what was the cost price of the plot?

(8) Mr. Jojo buys 30 articles for $1 and sells 29 articles for $1. Find the profit in percent.

(9) For how much should he sell the bicycle to get a profit of 19%, if a shopkeeper loses 20% by selling it for $688?

(10) How much percent will Peter earn if he buys 37 articles for $1 and sells 36 articles for $1?