Profit And Loss
Math MCQs

Question :    If a peddler buys 46 articles for $1 and sells 45 articles for $1 then, find the earnings in percentage.

Correct Answer  2.22%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 46 articles = $1

The Sale Price (SP) for 45 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 46 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₄₆

∵ The Sale Price (SP) for 45 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₄₅

Calculation of profit

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

= ¹/₄₅ – ¹/₄₆

= ^{46 – 45}/₂₀₇₀

⇒ Profit = ¹/₂₀₇₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₄₆, the the profit = ¹/₂₀₇₀

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

= ^{1/₂₀₇₀}/_¹/46

= ¹/₂₀₇₀ × ⁴⁶/₁

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

= ¹/₂₀₇₀ × ⁴⁶/₁ × 100

= ^{1 × 46 × 100}/_{2070 × 1}

= ⁴⁶⁰⁰/₂₀₇₀ = 2.22

Thus, Profit = 2.22% 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 46 articles = $1

And, the Sale Price (SP) of 45 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 46 and 45 = 2070

Now, Let total number of articles purchased = 2070

Here, since the Cost Price of 46 articles = $1

∴ the Cost Price of 1 articles = ¹/₄₆

Therefore, the Cost Price of 2070 articles

And, since the Sale Price of 45 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₄₅

Therefore, the Sale Price of 2070 articles

= ¹/₄₅ × 2070 = $46

⇒ The Sale Price (SP) of 2070 articles = $46

Now, the Cost Price (CP) of 2070 articles = $45

And, the Sale Price (SP) of 2070 articles = $46

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)

= 46 – 45 = 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}/₄₅

= ¹⁰⁰/₄₅ = 2.22

Thus, profit = 2.22% Answer

Similar Questions

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

(2) If after selling 5 bags of rice for $1297.20 a shopkeeper gets a loss of 8% then what was the cost price of the rice?

(3) John loses 63% by selling an article for $1113.70. For how much should he sell it to get a profit of 62%?

(4) Calculate the earnings in percent if Mr. Peter buys 66 articles for $1 and sells 65 articles for $1.

(5) Find the cost price, if a dealer gets a loss of 32% by selling 500 books for $4222.80.

(6) Mr. Razor loses 45% by selling an article for $1160.50. For how much should he sell it to get a profit of 44%?

(7) John purchased a bicycle in an auction at $80 and sold it at $104. Calculate the profit and profit percent in this sale.

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

(9) What was the cost price, if a trader gets a loss of 18% by selling some articles for $2796.20?

(10) Find the cost price, if a trader gets a loss of 37% by selling 500 packets of fruits for $4542.30