Profit And Loss
Math MCQs

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

Correct Answer  2.17%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 47 articles = $1

The Sale Price (SP) for 46 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 47 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₄₇

∵ The Sale Price (SP) for 46 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₄₆

Calculation of profit

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

= ¹/₄₆ – ¹/₄₇

= ^{47 – 46}/₂₁₆₂

⇒ Profit = ¹/₂₁₆₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₄₇, the the profit = ¹/₂₁₆₂

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

= ^{1/₂₁₆₂}/_¹/47

= ¹/₂₁₆₂ × ⁴⁷/₁

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

= ¹/₂₁₆₂ × ⁴⁷/₁ × 100

= ^{1 × 47 × 100}/_{2162 × 1}

= ⁴⁷⁰⁰/₂₁₆₂ = 2.17

Thus, Profit = 2.17% 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 47 articles = $1

And, the Sale Price (SP) of 46 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 47 and 46 = 2162

Now, Let total number of articles purchased = 2162

Here, since the Cost Price of 47 articles = $1

∴ the Cost Price of 1 articles = ¹/₄₇

Therefore, the Cost Price of 2162 articles

And, since the Sale Price of 46 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₄₆

Therefore, the Sale Price of 2162 articles

= ¹/₄₆ × 2162 = $47

⇒ The Sale Price (SP) of 2162 articles = $47

Now, the Cost Price (CP) of 2162 articles = $46

And, the Sale Price (SP) of 2162 articles = $47

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)

= 47 – 46 = 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}/₄₆

= ¹⁰⁰/₄₆ = 2.17

Thus, profit = 2.17% Answer

Similar Questions

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(2) By selling some items for $1788.90 a vendor gets a loss of 11%. Find the cost price of those items.

(3) Find the cost price, if a trader gets a loss of 73% by selling 100 bags of apples for $3890.70 then find the cost price of the apples.

(4) After selling some articles for $22269.00 a trader earns a profit of 290%. Find the cost price.

(5) What was the cost price, if a trader gets a loss of 18% by selling some articles for $2796.20?

(6) If a book seller gets a loss of 33% by selling 300 books for $4294.70 then find the cost price of the books.

(7) Find the cost price, if by selling some articles for $13792 a trader earns a profit of 220%

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

(9) William loses 43% by selling an article for $1145.70. For how much should he sell it to get a profit of 42%?

(10) What will be the cost price, if a trader gets a loss of 2% by selling an article for $205.80?