Profit And Loss
Math MCQs

Question :    Mr. John buys 28 articles for $1 and sells 27 articles for $1 then, find his profit percent.

Correct Answer  3.7%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 28 articles = $1

The Sale Price (SP) for 27 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 28 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₂₈

∵ The Sale Price (SP) for 27 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₂₇

Calculation of profit

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

= ¹/₂₇ – ¹/₂₈

= ^{28 – 27}/₇₅₆

⇒ Profit = ¹/₇₅₆

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₂₈, the the profit = ¹/₇₅₆

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

= ^1/₇₅₆/_¹/28

= ¹/₇₅₆ × ²⁸/₁

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

= ¹/₇₅₆ × ²⁸/₁ × 100

= ^{1 × 28 × 100}/_{756 × 1}

= ²⁸⁰⁰/₇₅₆ = 3.7

Thus, Profit = 3.7% 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 28 articles = $1

And, the Sale Price (SP) of 27 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 28 and 27 = 756

Now, Let total number of articles purchased = 756

Here, since the Cost Price of 28 articles = $1

∴ the Cost Price of 1 articles = ¹/₂₈

Therefore, the Cost Price of 756 articles

And, since the Sale Price of 27 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₂₇

Therefore, the Sale Price of 756 articles

= ¹/₂₇ × 756 = $28

⇒ The Sale Price (SP) of 756 articles = $28

Now, the Cost Price (CP) of 756 articles = $27

And, the Sale Price (SP) of 756 articles = $28

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)

= 28 – 27 = 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}/₂₇

= ¹⁰⁰/₂₇ = 3.7

Thus, profit = 3.7% Answer

Similar Questions

(1) If a hawker bought 63 candies for $1 and sold them at a rate of 62 candies per $1 then, find the profit percent.

(2) A share broker earns a profit of 400% by selling his shares for $39550. For how much had he purchased those shares?

(3) Mr. Donald loses 87% by selling an article for $547.30. For how much should he sell it to get a profit of 86%?

(4) John gets a 20% profit after selling his laptop for $372. What was the cost price of the laptop?

(5) What will be the earnings in percent if a vendor buys 45 articles for $1 and sells 44 articles for $1?

(6) Bill sold a bicycle for $640. If he purchased it at $800, then calculate his loss and loss percent in this sale.

(7) John loses 62% by selling an article for $1124.80. For how much should he sell it to get a profit of 61%?

(8) What will be the profit percentage if a hawker buys 64 articles for $1 and sells 63 articles for $1?

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

(10) How much percent will a vendor earn, if he buys 35 articles for $1 and sells 34 articles for $1?