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) Calculate the profit in percent if Mr. John buys 67 articles for $1 and sells 66 articles for $1.

(2) John purchased a bike for $500 and he sold it at a gain of 12%. Find the sale price of the bike.

(3) If Mr. Steve buys 41 articles for $1 and sells 40 articles for $1 then find the profit percent.

(4) If a vendor buys 60 articles for $1 and sells 59 articles for $1 then, calculate the profit in percent.

(5) If a shopkeeper loses 38% by selling some articles for $1091.20 then, he should sell them to get a profit of 37% for how much?

(6) By selling some items for $1788.90 a vendor gets a loss of 11%. Find the cost price of those items.

(7) Find the cost price, if a trader gets a loss of 59% by selling five TV sets for $4760.10

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

(9) Find the earnings percentage if a vendor buys 53 articles for $1 and sells 52 articles for $1.

(10) A dealer sold a plot for $26502.00. In this deal, if the dealer earns a profit of 320%, then find the cost price.