Profit And Loss
Math MCQs

Question :    For how much should Mr. John sell it to get a profit of 3% if he loses 4% by selling an article for $57.60?

Correct Answer  61.8

Solution & Explanation

Strategy to solve the question

Step (1) Calculate the cost price at given loss percent and the sale price.

Step (2) After gettting the cost price find the sale price at given profit percent.

Solution

Method (1) Formula Method

Finding the Sale Price to earn a profit using formula when the Sale Price at a loss is given

Given, the sale price (SP) = $57.6

And, the loss = 4%

Then, the Sale Price (SP) to earn a profit of 3% = ?

Formula to find the cost price when the sale price and loss percent are known

Cost Price (CP) = ¹⁰⁰/_{100 – gain%} × SP

Thus, the Cost Price (CP)

= ¹⁰⁰/_{100 – 4} × 57.6

= ¹⁰⁰/₉₆ × 57.6

= ^{100 × 57.6}/₉₆

= ⁵⁷⁶⁰/₉₆ = 60

Thus, the Cost Price (CP) = $60

Finding the Sale Price using the formula when the cost price and Profit percent are known

Here now, CP = $60

And, profit = 3%

Thus Sale Price (SP) = ?

Formula to find the Sale Price (SP) when the cost price (CP) and profit percent are known

Sale Price (SP) = ^{100 + gain%}/₁₀₀ × Cost Price (CP)

Thus, the Sale Price (SP)

= ^{100 + 3}/₁₀₀ × 60

= ¹⁰³/₁₀₀ × 60

= ^{103 × 60}/₁₀₀

= ⁶¹⁸⁰/₁₀₀ = 61.8

Thus, Sale Price (SP) at a profit of 3% = $61.8 Answer

Method (2) Algebraic Method

Finding the Sale Price (SP) to earn the given profit using the Algebraic Method when the Sale Pric (SP) at a loss percent is given

Given, the sale price (SP) = $57.6

And, the loss = 4%

Then, the Sale Price (SP) to earn a profit of 3% = ?

Let the Cost Price (CP) = m

Here given loss = 4%

Calculation of loss

loss is calculated on cost price (CP)

Formula to find the loss = loss% of CP

Thus, loss on the cost price of m

= 4% of m

= 4% × m

= ⁴/₁₀₀ × m

⇒ loss = ^{4 m}/₁₀₀

Calculation of Cost Price (CP)

The Sale Price (SP) = Cost Price (CP) – loss

⇒ 57.6 = m – ^{4 m}/₁₀₀

⇒ 57.6 = ^{100 m – 4 m}/₁₀₀

⇒ 57.6 = ^{96 m}/₁₀₀

After cross multiplication, we get

57.6 × 100 = 96 m

⇒ 96 m = 57.6 × 100

⇒ m = ^{57.6 × 100}/₉₆

⇒ m = ⁵⁷⁶⁰/₉₆ = 60

⇒ m = 60

Thus, the Cost Price (CP) = $60

Finding the Sale Price (SP) when the Cost Price (CP) and profit percent are known

Now, here, Cost Price = 60

And, the profit = 3%

Thus, Sale Price (SP)

= Cost Price (CP) + 3% of Cost Price (CP)

= 60 + ³/₁₀₀ × 60

= 60 + ^{3 × 60}/₁₀₀

= 60 + ¹⁸⁰/₁₀₀

= 60 + 1.8 = 61.8

Thus, Sale Price (SP) at a profit of 3% = $61.8 Answer

Method (3) Unitary Method

Finding the Sale Price (SP) to earn a given profit when the Sale price (SP) at a loss is given

Given, the sale price (SP) = $57.6

And, the loss = 4%

Then, the Sale Price (SP) to earn a profit of 3% = ?

Let, CP = 100

3% profit = 3% of CP

= 3% of 100 = 3

Thus, Sale Price to earn a profit of 3% = CP + 3

= 100 + 3 = 103

⇒ Sale Price to earn a profit of 3% = 103

4% loss = 4% of CP

= 4% of 100 = 4

Thus, Sale Price at a loss of 4% = CP – Loss

= 100 – 4 = 96

⇒ Sale Price at a loss of 4% = 96

∵ If the Sale Price is 96, then to earn a profit of 3% the Sale Price should be = 103

∴ If the Sale Price is 1, then to earn a profit of 3% the Sale Price should be

= ¹⁰³/₉₆

∴ If the Sale Price is 57.6, then to earn a profit of 3% the Sale Price should be

= ¹⁰³/₉₆ × 57.6

= ^{103 × 57.6}/₉₆

= ^5932.8/₉₆ = 61.8

Thus, Sale Price to get a profit of 3% = $61.8 Answer

Method (4) Shortcut Method

Shortcut Method to find the Sale Price at a given profit when Sale Price at a loss is given

Given, the sale price (SP) = $57.6

And, the loss = 4%

Then, the Sale Price (SP) to earn a profit of 3% = ?

Here, the Sale Price at a loss of 4 = $57.6

This means 96% of the Cost Price (CP) = 57.6

Therefore, 1% of the Cost Price (CP) = ^57.6/₉₆

Therefore, 100% of the Cost Price (CP)

= ^57.6/₉₆ × 100 = 60

Thus, the Cost Price (CP) = $60

Now, we need to find the Sale Price at a profit of 3%

Thus, Sale Price at a profit of 3%

= 103% of the Cost Price (CP)

= 103% of 60

= ¹⁰³/₁₀₀ × 60 = 61.8

Thus, the Cost Price at a profit of 3% = $61.8 Answer

Similar Questions

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(2) A trader loses 47% by selling an article for $1171.30. For how much should he sell it to get a profit of 46%?

(3) In an auction, Mr. Jojo got $27242.5 for his antique bike. If he got a profit of 325% in this deal, then what was his cost price.?

(4) A shopkeeper earns a profit of 175% by selling some antique articles for $9377.50. What was the cost price of those antique articles?

(5) Find the cost price, if Mrs. Barbara earns a profit of 275% by selling some items for $20287.50

(6) The cost price of an article is $12, and the sale price is $15. Find the profit and profit percent.

(7) If a shopkeeper loses 38% by selling some articles for $1091.20 then, he should sell them to get a profit of 37% for how much?

(8) Find the cost price, if a trader gets a loss of 50% by selling 500 bags of rice for $4905

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

(10) How much percent will a vendor earn if he buys 36 articles for $1 and sells them at a rate of 35 articles per $1?