Profit And Loss
Math MCQs

Question :    A trader loses 42% by selling an article for $1136.80. For how much should he sell it to get a profit of 41%?

Correct Answer  2763.6

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) = $1136.8

And, the loss = 42%

Then, the Sale Price (SP) to earn a profit of 41% = ?

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 – 42} × 1136.8

= ¹⁰⁰/₅₈ × 1136.8

= ^{100 × 1136.8}/₅₈

= ¹¹³⁶⁸⁰/₅₈ = 1960

Thus, the Cost Price (CP) = $1960

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

Here now, CP = $1960

And, profit = 41%

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 + 41}/₁₀₀ × 1960

= ¹⁴¹/₁₀₀ × 1960

= ^{141 × 1960}/₁₀₀

= ²⁷⁶³⁶⁰/₁₀₀ = 2763.6

Thus, Sale Price (SP) at a profit of 41% = $2763.6 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) = $1136.8

And, the loss = 42%

Then, the Sale Price (SP) to earn a profit of 41% = ?

Let the Cost Price (CP) = m

Here given loss = 42%

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

= 42% of m

= 42% × m

= ⁴²/₁₀₀ × m

⇒ loss = ^{42 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 1136.8 = m – ^{42 m}/₁₀₀

⇒ 1136.8 = ^{100 m – 42 m}/₁₀₀

⇒ 1136.8 = ^{58 m}/₁₀₀

After cross multiplication, we get

1136.8 × 100 = 58 m

⇒ 58 m = 1136.8 × 100

⇒ m = ^{1136.8 × 100}/₅₈

⇒ m = ¹¹³⁶⁸⁰/₅₈ = 1960

⇒ m = 1960

Thus, the Cost Price (CP) = $1960

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

Now, here, Cost Price = 1960

And, the profit = 41%

Thus, Sale Price (SP)

= Cost Price (CP) + 41% of Cost Price (CP)

= 1960 + ⁴¹/₁₀₀ × 1960

= 1960 + ^{41 × 1960}/₁₀₀

= 1960 + ⁸⁰³⁶⁰/₁₀₀

= 1960 + 803.6 = 2763.6

Thus, Sale Price (SP) at a profit of 41% = $2763.6 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) = $1136.8

And, the loss = 42%

Then, the Sale Price (SP) to earn a profit of 41% = ?

Let, CP = 100

41% profit = 41% of CP

= 41% of 100 = 41

Thus, Sale Price to earn a profit of 41% = CP + 41

= 100 + 41 = 141

⇒ Sale Price to earn a profit of 41% = 141

42% loss = 42% of CP

= 42% of 100 = 42

Thus, Sale Price at a loss of 42% = CP – Loss

= 100 – 42 = 58

⇒ Sale Price at a loss of 42% = 58

∵ If the Sale Price is 58, then to earn a profit of 41% the Sale Price should be = 141

∴ If the Sale Price is 1, then to earn a profit of 41% the Sale Price should be

= ¹⁴¹/₅₈

∴ If the Sale Price is 1136.8, then to earn a profit of 41% the Sale Price should be

= ¹⁴¹/₅₈ × 1136.8

= ^{141 × 1136.8}/₅₈

= ^160288.8/₅₈ = 2763.6

Thus, Sale Price to get a profit of 41% = $2763.6 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) = $1136.8

And, the loss = 42%

Then, the Sale Price (SP) to earn a profit of 41% = ?

Here, the Sale Price at a loss of 42 = $1136.8

This means 58% of the Cost Price (CP) = 1136.8

Therefore, 1% of the Cost Price (CP) = ^1136.8/₅₈

Therefore, 100% of the Cost Price (CP)

= ^1136.8/₅₈ × 100 = 1960

Thus, the Cost Price (CP) = $1960

Now, we need to find the Sale Price at a profit of 41%

Thus, Sale Price at a profit of 41%

= 141% of the Cost Price (CP)

= 141% of 1960

= ¹⁴¹/₁₀₀ × 1960 = 2763.6

Thus, the Cost Price at a profit of 41% = $2763.6 Answer

Similar Questions

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(2) Find the cost price, if Mr. Oliver earns a profit of 150% by selling an article for $7275.00

(3) A trader loses 53% by selling an article for $1179.70. For how much should he sell it to get a profit of 52%?

(4) Find the cost price, if a fruit seller gets a loss of 43% by selling 500 bags of fruits for $4793.70

(5) If a hawker buys buys 61 oranges for $1 and sells them at a rate of 60 oranges per $1 then, find the profit percent.

(6) Calculate the earnings in percent if a vendor buys 72 coins for $1 and sells 71 coins for $1.

(7) Mr. Peter loses 44% by selling an article for $1153.60. For how much should he sell it to get a profit of 43%?

(8) After selling an article for $282.10, a shopkeeper gets a loss of 9%. Thus, to earn a profit of 8% he should sell it at which price?

(9) Find the cost price, if a trader gets a loss of 19% by selling an article for $2924.10

(10) Mr. Peter earns a profit of 110% by selling goods for $4431.00. For how much was he purchased those goods?