Profit And Loss
Math MCQs

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

Correct Answer  1.33%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 76 articles = $1

The Sale Price (SP) for 75 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 76 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₇₆

∵ The Sale Price (SP) for 75 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₇₅

Calculation of profit

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

= ¹/₇₅ – ¹/₇₆

= ^{76 – 75}/₅₇₀₀

⇒ Profit = ¹/₅₇₀₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₇₆, the the profit = ¹/₅₇₀₀

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

= ^{1/₅₇₀₀}/_¹/76

= ¹/₅₇₀₀ × ⁷⁶/₁

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

= ¹/₅₇₀₀ × ⁷⁶/₁ × 100

= ^{1 × 76 × 100}/_{5700 × 1}

= ⁷⁶⁰⁰/₅₇₀₀ = 1.33

Thus, Profit = 1.33% 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 76 articles = $1

And, the Sale Price (SP) of 75 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 76 and 75 = 5700

Now, Let total number of articles purchased = 5700

Here, since the Cost Price of 76 articles = $1

∴ the Cost Price of 1 articles = ¹/₇₆

Therefore, the Cost Price of 5700 articles

And, since the Sale Price of 75 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₇₅

Therefore, the Sale Price of 5700 articles

= ¹/₇₅ × 5700 = $76

⇒ The Sale Price (SP) of 5700 articles = $76

Now, the Cost Price (CP) of 5700 articles = $75

And, the Sale Price (SP) of 5700 articles = $76

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)

= 76 – 75 = 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}/₇₅

= ¹⁰⁰/₇₅ = 1.33

Thus, profit = 1.33% Answer

Similar Questions

(1) While shifting to the other city, Mr. Bob sold all of the furniture and got a profit of 35%. If he sold them for $823.50, then for how much had he purchased them?

(2) Find the cost price, if a trader gets a loss of 45% by selling 800 bags of fruits for $4845.50

(3) Noah loses 78% by selling an article for $827.20. For how much should he sell it to get a profit of 77%?

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

(5) Find the cost price, if a share broker gets a loss of 26% by selling 100 shares for $3707.40.

(6) Find the cost price, if a broker earns a profit of 370% by selling an old house for $34357

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

(8) If a vendor bought 62 candies for $1 and sold 61 candies per $1 then find the profit percent.

(9) A pddler buys 47 candies for $1 and sells at a rate of 46 candies per $1 then find the profit percent.

(10) What is the cost price; if a trader earns a profit of 295% by selling some articles for $22949.50?