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

(1) A trader loses 48% by selling an article for $1175.20. For how much should he sell it to get a profit of 47%?

(2) Mr. Boby loses 15% by selling an article for $518.50. For how much should he sell it to get a profit of 14%?

(3) If a vendor gets a loss of 21% by selling some apples for $3167.90 then what was the cost price of those apples?

(4) Calculate the earnings percentage if a vendor buys 55 articles for $1 and sells 54 articles for $1.

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

(6) Find the cost price, if a trader gets a loss of 41% by selling an article for $4725.90

(7) A dealer loses 58% by selling an article for $1159.20. For how much should he sell it to get a profit of 57%?

(8) A trader gets a loss of 52% by selling 500 bags of rice for $4900.80. Find the cost price of rice.

(9) For how much Mr. Peter should sell his books to get a profit of 11%? If he loses 12% by selling them for $404.80.

(10) Mollie purchased 150 kg of wheat at $1350. Due to some unavoidable circumstances, he had to sell the wheat at $7.20 per kg. Calculate his total loss and loss percent in this sale.