Profit And Loss
Math MCQs

Question :    If a vendor buys 14 chocolates for $1 and sells 13 chocolates for $1 then, what is his profit percent?

Correct Answer  7.69%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 14 articles = $1

The Sale Price (SP) for 13 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 14 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₁₄

∵ The Sale Price (SP) for 13 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₁₃

Calculation of profit

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

= ¹/₁₃ – ¹/₁₄

= ^{14 – 13}/₁₈₂

⇒ Profit = ¹/₁₈₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₁₄, the the profit = ¹/₁₈₂

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

= ^1/₁₈₂/_¹/14

= ¹/₁₈₂ × ¹⁴/₁

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

= ¹/₁₈₂ × ¹⁴/₁ × 100

= ^{1 × 14 × 100}/_{182 × 1}

= ¹⁴⁰⁰/₁₈₂ = 7.69

Thus, Profit = 7.69% 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 14 articles = $1

And, the Sale Price (SP) of 13 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 14 and 13 = 182

Now, Let total number of articles purchased = 182

Here, since the Cost Price of 14 articles = $1

∴ the Cost Price of 1 articles = ¹/₁₄

Therefore, the Cost Price of 182 articles

And, since the Sale Price of 13 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₁₃

Therefore, the Sale Price of 182 articles

= ¹/₁₃ × 182 = $14

⇒ The Sale Price (SP) of 182 articles = $14

Now, the Cost Price (CP) of 182 articles = $13

And, the Sale Price (SP) of 182 articles = $14

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)

= 14 – 13 = 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}/₁₃

= ¹⁰⁰/₁₃ = 7.69

Thus, profit = 7.69% Answer

Similar Questions

(1) Mr. John sold his scoory for $1465.10 and got a loss of 9%. What was the cost price of the scooty?

(2) Find the cost price, if Mrs. Mary earns a profit of 270% by selling some articles for $19647

(3) If a dealer earns a profit of 255% by selling some articles for $17785.50, then find the cost price.

(4) If Mr. Peter buys 17 apples for $1 and sells 16 apples for $1 then, find the profit percent in this sale.

(5) Jack sold a TV set at $1584. If he purchased it at $1800, then calculate his loss and loss percent in this sale.

(6) If a trader gets a loss of 24% by selling 500 shares for $3503.60 then find the cost price of those shares.

(7) Mike sold his car at a profit of 25%. If he purchased that car at $2500 then find the sale price of the car.

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

(9) If a vendor buys 60 articles for $1 and sells 59 articles for $1 then, calculate the profit in percent.

(10) Find the cost price, if a trader gets a loss of 51% by selling 200 bags of rice for $4904.90