Profit And Loss
Math MCQs

Question :    What will be the earnings in percent if a hawker buys 59 articles for $1 and sells 58 articles for $1?

Correct Answer  1.72%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 59 articles = $1

The Sale Price (SP) for 58 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 59 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₅₉

∵ The Sale Price (SP) for 58 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₅₈

Calculation of profit

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

= ¹/₅₈ – ¹/₅₉

= ^{59 – 58}/₃₄₂₂

⇒ Profit = ¹/₃₄₂₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₅₉, the the profit = ¹/₃₄₂₂

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

= ^{1/₃₄₂₂}/_¹/59

= ¹/₃₄₂₂ × ⁵⁹/₁

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

= ¹/₃₄₂₂ × ⁵⁹/₁ × 100

= ^{1 × 59 × 100}/_{3422 × 1}

= ⁵⁹⁰⁰/₃₄₂₂ = 1.72

Thus, Profit = 1.72% 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 59 articles = $1

And, the Sale Price (SP) of 58 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 59 and 58 = 3422

Now, Let total number of articles purchased = 3422

Here, since the Cost Price of 59 articles = $1

∴ the Cost Price of 1 articles = ¹/₅₉

Therefore, the Cost Price of 3422 articles

And, since the Sale Price of 58 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₅₈

Therefore, the Sale Price of 3422 articles

= ¹/₅₈ × 3422 = $59

⇒ The Sale Price (SP) of 3422 articles = $59

Now, the Cost Price (CP) of 3422 articles = $58

And, the Sale Price (SP) of 3422 articles = $59

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)

= 59 – 58 = 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}/₅₈

= ¹⁰⁰/₅₈ = 1.72

Thus, profit = 1.72% Answer

Similar Questions

(1) 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?

(2) Find the cost price, if a trader earns a profit of 395% by selling an article for $38659.5

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

(4) Find the cost price, if a dealer gets a loss of 31% by selling 400 stocks for $4146.90

(5) For how much should a trader sell an item to get a profit of 49% if he loses 50% by selling it for $1180.00?

(6) Noah loses 77% by selling an article for $853.30. For how much should he sell it to get a profit of 76%?

(7) A trader loses 42% by selling an article for $1136.80. For how much should he sell it to get a profit of 41%?

(8) For how much Mr. Peter should sell his books to get a profit of 11%? If he loses 12% by selling them for $404.80.

(9) James loses 67% by selling an article for $1059.30. For how much should he sell it to get a profit of 66%?

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