Profit And Loss
Math MCQs

Question :    How much percent will John get if he buys 38 articles for $1 and sells 37 articles for $1?

Correct Answer  2.7%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 38 articles = $1

The Sale Price (SP) for 37 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 38 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₃₈

∵ The Sale Price (SP) for 37 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₃₇

Calculation of profit

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

= ¹/₃₇ – ¹/₃₈

= ^{38 – 37}/₁₄₀₆

⇒ Profit = ¹/₁₄₀₆

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₃₈, the the profit = ¹/₁₄₀₆

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

= ^{1/₁₄₀₆}/_¹/38

= ¹/₁₄₀₆ × ³⁸/₁

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

= ¹/₁₄₀₆ × ³⁸/₁ × 100

= ^{1 × 38 × 100}/_{1406 × 1}

= ³⁸⁰⁰/₁₄₀₆ = 2.7

Thus, Profit = 2.7% 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 38 articles = $1

And, the Sale Price (SP) of 37 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 38 and 37 = 1406

Now, Let total number of articles purchased = 1406

Here, since the Cost Price of 38 articles = $1

∴ the Cost Price of 1 articles = ¹/₃₈

Therefore, the Cost Price of 1406 articles

And, since the Sale Price of 37 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₃₇

Therefore, the Sale Price of 1406 articles

= ¹/₃₇ × 1406 = $38

⇒ The Sale Price (SP) of 1406 articles = $38

Now, the Cost Price (CP) of 1406 articles = $37

And, the Sale Price (SP) of 1406 articles = $38

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)

= 38 – 37 = 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}/₃₇

= ¹⁰⁰/₃₇ = 2.7

Thus, profit = 2.7% Answer

Similar Questions

(1) After selling some articles for $22269.00 a trader earns a profit of 290%. Find the cost price.

(2) Bill sold his secondhand motorcycle for $512.50. In this sale, he got a profit of 25%. For how much amount had he purchased the motorcycle?

(3) Find the cost price, if a dealer gets a loss of 30% by selling 300 stocks for $4067

(4) Find the cost price of the plot, if a dealer earns a profit of 185% by selling the plot for $10288.5

(5) A seller gets a profit of 7% by selling a TV set for $4280. If he would have sold it for $4200, then find his profit percent.

(6) Find the cost price, if Mr. Oliver earns a profit of 150% by selling an article for $7275.00

(7) A share broker earns a profit of 400% by selling his shares for $39550. For how much had he purchased those shares?

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

(9) if a vendor bought 74 nibs for $1 and sells them at a rate of 73 per $1 then calculate the profit in percent.

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