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

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(2) Find the cost price if a broker earned 375% while dealing a house for $35197.50

(3) If a trader gets a loss of 71% by selling 150 bags of corn flakes for $4062.90 then find the cost price of the corn flakes.

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

(5) What will be thr profit in percent if a vendor purchased 76 pins for $1 and sold 75 pins for $1?

(6) After selling an article for $1565.5 the shopkeeper earns a profit of 55%. For how much had he purchase that article?

(7) Find the cost price, if Mrs. Olivia earns a profit of 160% by selling some articles for $8086

(8) How much percent will John get if he buys 38 articles for $1 and sells 37 articles for $1?

(9) 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?

(10) What will be the cost price if a shopkeeper sells some clothes for $994 and earns a profit of 40%?