Profit And Loss
Math MCQs

Question :    If a vendor buys 7 lemons for $1 and sells 6 lemons for $1 then, what is the profit percent in this sale?

Correct Answer  16.67%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 7 articles = $1

The Sale Price (SP) for 6 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 7 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₇

∵ The Sale Price (SP) for 6 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₆

Calculation of profit

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

= ¹/₆ – ¹/₇

= ^{7 – 6}/₄₂

⇒ Profit = ¹/₄₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₇, the the profit = ¹/₄₂

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

= ^1/₄₂/_¹/7

= ¹/₄₂ × ⁷/₁

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

= ¹/₄₂ × ⁷/₁ × 100

= ^{1 × 7 × 100}/_{42 × 1}

= ⁷⁰⁰/₄₂ = 16.67

Thus, Profit = 16.67% 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 7 articles = $1

And, the Sale Price (SP) of 6 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 7 and 6 = 42

Now, Let total number of articles purchased = 42

Here, since the Cost Price of 7 articles = $1

∴ the Cost Price of 1 articles = ¹/₇

Therefore, the Cost Price of 42 articles

And, since the Sale Price of 6 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₆

Therefore, the Sale Price of 42 articles

= ¹/₆ × 42 = $7

⇒ The Sale Price (SP) of 42 articles = $7

Now, the Cost Price (CP) of 42 articles = $6

And, the Sale Price (SP) of 42 articles = $7

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)

= 7 – 6 = 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}/₆

= ¹⁰⁰/₆ = 16.67

Thus, profit = 16.67% Answer

Similar Questions

(1) If a shopkeeper earns a profit of 5% by selling an article at $210, then find the cost price of that article.

(2) To get a profit of 15% Mr. John should sell his old bicycle for how much, if he loses 16% by selling it for $554.40?

(3) Find the cost price, if a vendor gets a loss of 15% by selling some articles for $2388.50.

(4) Mr. Bobby earns a profit of 120% by selling a TV set for $5082. What was the cost price of the TV set?

(5) Find the cost price, if a trader gets a loss of 48% by selling 500 kg of rice for $4893.20

(6) Find the cost price, if a trader gets a loss of 49% by selling 1500 kg rice for $4901.10

(7) Find the cost price, if a trader gets a loss of 39% by selling 100 packets of fruits for $4642.10

(8) Find the cost price, if a trader gets a loss of 47% by selling 500 kg rice for $4881.30

(9) A shopkeeper loses 27% by selling some articles for $883.30. For how much should he sell them to get a profit of 26%?

(10) Find the cost price, if a share broker gets a loss of 29% by selling 500 stocks for $3983.10