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) Mr. Jack buys 13 articles for $1 and sells 12 articles for $1. Find his profit percent.

(2) Mr. John sold his scoory for $1465.10 and got a loss of 9%. What was the cost price of the scooty?

(3) Mr. Oliver loses 79% by selling an article for $800.10. For how much should he sell it to get a profit of 78%?

(4) If a trader gets a loss of 24% by selling 500 shares for $3503.60 then find the cost price of those shares.

(5) A hawker buys 10 articles for $1 and sells 9 articles for $1 then, find the profit percent.

(6) By selling an article for $1125.30 a vendor gets a loss of 7%. Calculate the cost price.

(7) Noah loses 78% by selling an article for $827.20. For how much should he sell it to get a profit of 77%?

(8) A dealer loses 56% by selling an article for $1170.40. For how much should he sell it to get a profit of 55%?

(9) If a shopkeeper gets a loss of 65% by selling five TV sets for $4483.50 then find the cost price of all those TV sets.

(10) A shopkeeper loses 46% by selling an article for $1166.40. For how much should he sell it to get a profit of 45%?