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

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(2) Calculate the earnings in percent if a hawker buys 44 articles for $1 and sells 43 articles for $1.

(3) A fruit seller gets a loss of 6% by selling an his old stock for $949.40. What was his cost price?

(4) A street seller buys 8 articles for $1 and sells 7 articles for $1. Find the profit percent in this sale.

(5) Mr. Oliver loses 79% by selling an article for $800.10. For how much should he sell it to get a profit of 78%?

(6) If a trader gets a loss of 16% by selling some articles for $2528.40 then find the cost price.

(7) Find the earnings percentage if a hawker buys 50 articles for $1 and sells 49 articles for $1.

(8) What is the cost price if a trader earns a profit of 155% by selling an article for $7675.50

(9) John purchased a bike for $500 and he sold it at a gain of 12%. Find the sale price of the bike.

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