Profit And Loss
Math MCQs

Question :    Calculate the earnings percentage if a vendor buys 55 articles for $1 and sells 54 articles for $1.

Correct Answer  1.85%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 55 articles = $1

The Sale Price (SP) for 54 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 55 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₅₅

∵ The Sale Price (SP) for 54 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₅₄

Calculation of profit

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

= ¹/₅₄ – ¹/₅₅

= ^{55 – 54}/₂₉₇₀

⇒ Profit = ¹/₂₉₇₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₅₅, the the profit = ¹/₂₉₇₀

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

= ^{1/₂₉₇₀}/_¹/55

= ¹/₂₉₇₀ × ⁵⁵/₁

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

= ¹/₂₉₇₀ × ⁵⁵/₁ × 100

= ^{1 × 55 × 100}/_{2970 × 1}

= ⁵⁵⁰⁰/₂₉₇₀ = 1.85

Thus, Profit = 1.85% 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 55 articles = $1

And, the Sale Price (SP) of 54 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 55 and 54 = 2970

Now, Let total number of articles purchased = 2970

Here, since the Cost Price of 55 articles = $1

∴ the Cost Price of 1 articles = ¹/₅₅

Therefore, the Cost Price of 2970 articles

And, since the Sale Price of 54 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₅₄

Therefore, the Sale Price of 2970 articles

= ¹/₅₄ × 2970 = $55

⇒ The Sale Price (SP) of 2970 articles = $55

Now, the Cost Price (CP) of 2970 articles = $54

And, the Sale Price (SP) of 2970 articles = $55

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)

= 55 – 54 = 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}/₅₄

= ¹⁰⁰/₅₄ = 1.85

Thus, profit = 1.85% Answer

Similar Questions

(1) Bill sold his bicycle at a profit of 15%. If he purchased that bicycle at $200 then find the sale price of the cycle.

(2) If a shopkeeper loses 6% by selling some items for $150.40 then, for how much should he sell them to get a profit of 5%?

(3) Peter buys 5 articles for $1 and sells 4 articles for $1. Find the profit percent in this sale.

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

(5) Find the profit percent if a vendor buys 9 articles for $1 and sells 8 articles for $1.

(6) Find the cost price, if a shopkeeper earns a profit of 240% by selling an article for $16014

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

(8) Mr. John buys 28 articles for $1 and sells 27 articles for $1 then, find his profit percent.

(9) After selling an article for $282.10, a shopkeeper gets a loss of 9%. Thus, to earn a profit of 8% he should sell it at which price?

(10) Mr. Boby loses 15% by selling an article for $518.50. For how much should he sell it to get a profit of 14%?