Profit And Loss
Math MCQs

Question :    If a hawker bought 22 apples per $1 and sold them at a rate of 21 apples per $1, then what would his profit percent be?

Correct Answer  4.76%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 22 articles = $1

The Sale Price (SP) for 21 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 22 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₂₂

∵ The Sale Price (SP) for 21 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₂₁

Calculation of profit

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

= ¹/₂₁ – ¹/₂₂

= ^{22 – 21}/₄₆₂

⇒ Profit = ¹/₄₆₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₂₂, the the profit = ¹/₄₆₂

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

= ^1/₄₆₂/_¹/22

= ¹/₄₆₂ × ²²/₁

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

= ¹/₄₆₂ × ²²/₁ × 100

= ^{1 × 22 × 100}/_{462 × 1}

= ²²⁰⁰/₄₆₂ = 4.76

Thus, Profit = 4.76% 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 22 articles = $1

And, the Sale Price (SP) of 21 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 22 and 21 = 462

Now, Let total number of articles purchased = 462

Here, since the Cost Price of 22 articles = $1

∴ the Cost Price of 1 articles = ¹/₂₂

Therefore, the Cost Price of 462 articles

And, since the Sale Price of 21 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₂₁

Therefore, the Sale Price of 462 articles

= ¹/₂₁ × 462 = $22

⇒ The Sale Price (SP) of 462 articles = $22

Now, the Cost Price (CP) of 462 articles = $21

And, the Sale Price (SP) of 462 articles = $22

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)

= 22 – 21 = 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}/₂₁

= ¹⁰⁰/₂₁ = 4.76

Thus, profit = 4.76% Answer

Similar Questions

(1) Find the cost price, if Mr. Jojo earns a profit of 355% by selling some articles for $31895.5

(2) A shopkeeper loses 31% by selling an article for $972.90. For how much should he sell it to get a profit of 30%?

(3) A broker loses 41% by selling an article for $1126.90. For how much should he sell it to get a profit of 40%?

(4) William loses 74% by selling an article for $925.60. For how much should he sell it to get a profit of 73%?

(5) Find the cost price if Mr. Rocky earns a profit of 105% by selling an article for $4120.50

(6) For how much should Mr. Bose sell his furniture to get a profit of 28%, if he loses 29% by selling it for $930.10?

(7) If a shopkeeper loses 6% by selling some items for $150.40 then, for how much should he sell them to get a profit of 5%?

(8) If a trader gets a loss of 13% by selling some colthes for $2096.70 then find the cost price.

(9) Find the cost price, if a vendor gets a loss of 56% by selling a TV set for $4844.40.

(10) John sold rice at $7.20 per kg. If he purchased 120 kg of rice for $960, then calculate the loss and loss percent in this sale.