Profit And Loss
Math MCQs

Question :    A shopkeeper loses 40% by selling an article for $1116.00. For how much should he sell it to get a profit of 39%?

Correct Answer  2585.4

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) = $1116

And, the loss = 40%

Then, the Sale Price (SP) to earn a profit of 39% = ?

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 – 40} × 1116

= ¹⁰⁰/₆₀ × 1116

= ^{100 × 1116}/₆₀

= ¹¹¹⁶⁰⁰/₆₀ = 1860

Thus, the Cost Price (CP) = $1860

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

Here now, CP = $1860

And, profit = 39%

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 + 39}/₁₀₀ × 1860

= ¹³⁹/₁₀₀ × 1860

= ^{139 × 1860}/₁₀₀

= ²⁵⁸⁵⁴⁰/₁₀₀ = 2585.4

Thus, Sale Price (SP) at a profit of 39% = $2585.4 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) = $1116

And, the loss = 40%

Then, the Sale Price (SP) to earn a profit of 39% = ?

Let the Cost Price (CP) = m

Here given loss = 40%

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

= 40% of m

= 40% × m

= ⁴⁰/₁₀₀ × m

⇒ loss = ^{40 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 1116 = m – ^{40 m}/₁₀₀

⇒ 1116 = ^{100 m – 40 m}/₁₀₀

⇒ 1116 = ^{60 m}/₁₀₀

After cross multiplication, we get

1116 × 100 = 60 m

⇒ 60 m = 1116 × 100

⇒ m = ^{1116 × 100}/₆₀

⇒ m = ¹¹¹⁶⁰⁰/₆₀ = 1860

⇒ m = 1860

Thus, the Cost Price (CP) = $1860

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

Now, here, Cost Price = 1860

And, the profit = 39%

Thus, Sale Price (SP)

= Cost Price (CP) + 39% of Cost Price (CP)

= 1860 + ³⁹/₁₀₀ × 1860

= 1860 + ^{39 × 1860}/₁₀₀

= 1860 + ⁷²⁵⁴⁰/₁₀₀

= 1860 + 725.4 = 2585.4

Thus, Sale Price (SP) at a profit of 39% = $2585.4 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) = $1116

And, the loss = 40%

Then, the Sale Price (SP) to earn a profit of 39% = ?

Let, CP = 100

39% profit = 39% of CP

= 39% of 100 = 39

Thus, Sale Price to earn a profit of 39% = CP + 39

= 100 + 39 = 139

⇒ Sale Price to earn a profit of 39% = 139

40% loss = 40% of CP

= 40% of 100 = 40

Thus, Sale Price at a loss of 40% = CP – Loss

= 100 – 40 = 60

⇒ Sale Price at a loss of 40% = 60

∵ If the Sale Price is 60, then to earn a profit of 39% the Sale Price should be = 139

∴ If the Sale Price is 1, then to earn a profit of 39% the Sale Price should be

= ¹³⁹/₆₀

∴ If the Sale Price is 1116, then to earn a profit of 39% the Sale Price should be

= ¹³⁹/₆₀ × 1116

= ^{139 × 1116}/₆₀

= ¹⁵⁵¹²⁴/₆₀ = 2585.4

Thus, Sale Price to get a profit of 39% = $2585.4 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) = $1116

And, the loss = 40%

Then, the Sale Price (SP) to earn a profit of 39% = ?

Here, the Sale Price at a loss of 40 = $1116

This means 60% of the Cost Price (CP) = 1116

Therefore, 1% of the Cost Price (CP) = ¹¹¹⁶/₆₀

Therefore, 100% of the Cost Price (CP)

= ¹¹¹⁶/₆₀ × 100 = 1860

Thus, the Cost Price (CP) = $1860

Now, we need to find the Sale Price at a profit of 39%

Thus, Sale Price at a profit of 39%

= 139% of the Cost Price (CP)

= 139% of 1860

= ¹³⁹/₁₀₀ × 1860 = 2585.4

Thus, the Cost Price at a profit of 39% = $2585.4 Answer

Similar Questions

(1) What is the cost price if Mrs. Norrah gets a profit of 165% by selling some items for $8506.5

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

(3) William loses 75% by selling an article for $902.50. For how much should he sell it to get a profit of 74%?

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

(5) Mr. Donald loses 84% by selling an article for $649.60. For how much should he sell it to get a profit of 83%?

(6) A dealer earns a profit of 285% by selling some items for $21598.50. What was his cost price?

(7) Find the cost price, if a trader gets a loss of 40% by selling 1000 packets of fruits for $4686

(8) What will be profit percent if John buys 6 articles for $1 and sells 5 articles for $1?

(9) A dealer loses 23% by selling an article for $777.7. For how much should he sell it to get a profit of 22%?

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