Profit And Loss
Math MCQs

Question :    Mr. William buys 15 toffees for $1 and sells 14 tofees for $1. What is the profit percent?

Correct Answer  7.14%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 15 articles = $1

The Sale Price (SP) for 14 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 15 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₁₅

∵ The Sale Price (SP) for 14 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₁₄

Calculation of profit

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

= ¹/₁₄ – ¹/₁₅

= ^{15 – 14}/₂₁₀

⇒ Profit = ¹/₂₁₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₁₅, the the profit = ¹/₂₁₀

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

= ^1/₂₁₀/_¹/15

= ¹/₂₁₀ × ¹⁵/₁

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

= ¹/₂₁₀ × ¹⁵/₁ × 100

= ^{1 × 15 × 100}/_{210 × 1}

= ¹⁵⁰⁰/₂₁₀ = 7.14

Thus, Profit = 7.14% 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 15 articles = $1

And, the Sale Price (SP) of 14 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 15 and 14 = 210

Now, Let total number of articles purchased = 210

Here, since the Cost Price of 15 articles = $1

∴ the Cost Price of 1 articles = ¹/₁₅

Therefore, the Cost Price of 210 articles

And, since the Sale Price of 14 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₁₄

Therefore, the Sale Price of 210 articles

= ¹/₁₄ × 210 = $15

⇒ The Sale Price (SP) of 210 articles = $15

Now, the Cost Price (CP) of 210 articles = $14

And, the Sale Price (SP) of 210 articles = $15

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)

= 15 – 14 = 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}/₁₄

= ¹⁰⁰/₁₄ = 7.14

Thus, profit = 7.14% Answer

Similar Questions

(1) After selling some antique items for $6504 a trader earns a profit of 140%. Find the cost price of those antique items.

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

(3) If a hawker buys 75 refill for $1 and sold them at a rate of 74 per $1 then calculate his profit in percentage.

(4) A car dealer earns 135% by selling an old antique car for $6133.50. For how much had he purchased that car?

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

(6) For how much should Mr. John sell it to get a profit of 3% if he loses 4% by selling an article for $57.60?

(7) Calculate the cost price, if a trader gets a loss of 3% by selling an article for $397.70

(8) A seller gets a profit of 7% by selling a TV set for $4280. If he would have sold it for $4200, then find his profit percent.

(9) A shopkeeper earns 130% after selling some old bikes for $5773. What was his cost price?

(10) By selling some goods for $3249 a shopkeeper earns a profit of 90%. Find the cost price of those goods.