Profit And Loss
Math MCQs

Question :    What will be the earnings in percent if a vendor buys 45 articles for $1 and sells 44 articles for $1?

Correct Answer  2.27%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 45 articles = $1

The Sale Price (SP) for 44 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 45 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₄₅

∵ The Sale Price (SP) for 44 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₄₄

Calculation of profit

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

= ¹/₄₄ – ¹/₄₅

= ^{45 – 44}/₁₉₈₀

⇒ Profit = ¹/₁₉₈₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₄₅, the the profit = ¹/₁₉₈₀

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

= ^{1/₁₉₈₀}/_¹/45

= ¹/₁₉₈₀ × ⁴⁵/₁

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

= ¹/₁₉₈₀ × ⁴⁵/₁ × 100

= ^{1 × 45 × 100}/_{1980 × 1}

= ⁴⁵⁰⁰/₁₉₈₀ = 2.27

Thus, Profit = 2.27% 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 45 articles = $1

And, the Sale Price (SP) of 44 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 45 and 44 = 1980

Now, Let total number of articles purchased = 1980

Here, since the Cost Price of 45 articles = $1

∴ the Cost Price of 1 articles = ¹/₄₅

Therefore, the Cost Price of 1980 articles

And, since the Sale Price of 44 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₄₄

Therefore, the Sale Price of 1980 articles

= ¹/₄₄ × 1980 = $45

⇒ The Sale Price (SP) of 1980 articles = $45

Now, the Cost Price (CP) of 1980 articles = $44

And, the Sale Price (SP) of 1980 articles = $45

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)

= 45 – 44 = 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}/₄₄

= ¹⁰⁰/₄₄ = 2.27

Thus, profit = 2.27% Answer

Similar Questions

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

(2) Mr. Steven loses 93% by selling an article for $315.70. For how much should he sell it to get a profit of 92%?

(3) Find the earnings percentage if a peddler buys 51 articles for $1 and sells 50 articles for $1.

(4) If a peddler buys 46 articles for $1 and sells 45 articles for $1 then, find the earnings in percentage.

(5) Find the cost price, if a trader gets a loss of 36% by selling 500 packets of fruits for $4486.40

(6) William loses 73% by selling an article for $947.70. For how much should he sell it to get a profit of 72%?

(7) If Mr. Jobby buys 18 kiwis for $1 and sells them at a rate of 17 per $1 then what would be the profit percent?.

(8) Bill sold a bicycle for $640. If he purchased it at $800, then calculate his loss and loss percent in this sale.

(9) If a shopkeeper gets a loss of 53% by selling 200 kg of rice for $4892.70 then find the cost price of rice.

(10) Mr. Oliver loses 34% by selling an article for $1029.60. For how much should he sell it to get a profit of 33%?