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) If a broker gets a loss of 22% by selling 100 shares for $3283.80, then find the cost price of those shares.

(2) Calculate the earnings percentage if a vendor buys 57 articles for $1 and sells 56 articles for $1.

(3) Mr. Donald loses 88% by selling an article for $511.20. For how much should he sell it to get a profit of 87%?

(4) Peter loses 32% by selling an article for $992.80. For how much should he sell it to get a profit of 31%?

(5) Mr. Jack gets a profit of 195% by selling some articles for $11239.50. What was his cost price?

(6) A shopkeeper loses 22% by selling an article for $748.80. For how much should he sell it to get a profit of 21%?

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

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

(9) Find the cost price, if a trader gets a loss of 46% by selling 500 kg rice for $4865.40

(10) Mr. Jack buys 13 articles for $1 and sells 12 articles for $1. Find his profit percent.