Profit And Loss
Math MCQs

Question :    If a broker loses 39% by selling some of his stocks for $1104.10 then he should sell them for how much to get a profit of 38%?

Correct Answer  2497.8

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) = $1104.1

And, the loss = 39%

Then, the Sale Price (SP) to earn a profit of 38% = ?

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 – 39} × 1104.1

= ¹⁰⁰/₆₁ × 1104.1

= ^{100 × 1104.1}/₆₁

= ¹¹⁰⁴¹⁰/₆₁ = 1810

Thus, the Cost Price (CP) = $1810

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

Here now, CP = $1810

And, profit = 38%

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 + 38}/₁₀₀ × 1810

= ¹³⁸/₁₀₀ × 1810

= ^{138 × 1810}/₁₀₀

= ²⁴⁹⁷⁸⁰/₁₀₀ = 2497.8

Thus, Sale Price (SP) at a profit of 38% = $2497.8 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) = $1104.1

And, the loss = 39%

Then, the Sale Price (SP) to earn a profit of 38% = ?

Let the Cost Price (CP) = m

Here given loss = 39%

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

= 39% of m

= 39% × m

= ³⁹/₁₀₀ × m

⇒ loss = ^{39 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 1104.1 = m – ^{39 m}/₁₀₀

⇒ 1104.1 = ^{100 m – 39 m}/₁₀₀

⇒ 1104.1 = ^{61 m}/₁₀₀

After cross multiplication, we get

1104.1 × 100 = 61 m

⇒ 61 m = 1104.1 × 100

⇒ m = ^{1104.1 × 100}/₆₁

⇒ m = ¹¹⁰⁴¹⁰/₆₁ = 1810

⇒ m = 1810

Thus, the Cost Price (CP) = $1810

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

Now, here, Cost Price = 1810

And, the profit = 38%

Thus, Sale Price (SP)

= Cost Price (CP) + 38% of Cost Price (CP)

= 1810 + ³⁸/₁₀₀ × 1810

= 1810 + ^{38 × 1810}/₁₀₀

= 1810 + ⁶⁸⁷⁸⁰/₁₀₀

= 1810 + 687.8 = 2497.8

Thus, Sale Price (SP) at a profit of 38% = $2497.8 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) = $1104.1

And, the loss = 39%

Then, the Sale Price (SP) to earn a profit of 38% = ?

Let, CP = 100

38% profit = 38% of CP

= 38% of 100 = 38

Thus, Sale Price to earn a profit of 38% = CP + 38

= 100 + 38 = 138

⇒ Sale Price to earn a profit of 38% = 138

39% loss = 39% of CP

= 39% of 100 = 39

Thus, Sale Price at a loss of 39% = CP – Loss

= 100 – 39 = 61

⇒ Sale Price at a loss of 39% = 61

∵ If the Sale Price is 61, then to earn a profit of 38% the Sale Price should be = 138

∴ If the Sale Price is 1, then to earn a profit of 38% the Sale Price should be

= ¹³⁸/₆₁

∴ If the Sale Price is 1104.1, then to earn a profit of 38% the Sale Price should be

= ¹³⁸/₆₁ × 1104.1

= ^{138 × 1104.1}/₆₁

= ^152365.8/₆₁ = 2497.8

Thus, Sale Price to get a profit of 38% = $2497.8 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) = $1104.1

And, the loss = 39%

Then, the Sale Price (SP) to earn a profit of 38% = ?

Here, the Sale Price at a loss of 39 = $1104.1

This means 61% of the Cost Price (CP) = 1104.1

Therefore, 1% of the Cost Price (CP) = ^1104.1/₆₁

Therefore, 100% of the Cost Price (CP)

= ^1104.1/₆₁ × 100 = 1810

Thus, the Cost Price (CP) = $1810

Now, we need to find the Sale Price at a profit of 38%

Thus, Sale Price at a profit of 38%

= 138% of the Cost Price (CP)

= 138% of 1810

= ¹³⁸/₁₀₀ × 1810 = 2497.8

Thus, the Cost Price at a profit of 38% = $2497.8 Answer

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