Profit And Loss
Math MCQs

Question :    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.

Correct Answer  510.6

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) = $404.8

And, the loss = 12%

Then, the Sale Price (SP) to earn a profit of 11% = ?

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 – 12} × 404.8

= ¹⁰⁰/₈₈ × 404.8

= ^{100 × 404.8}/₈₈

= ⁴⁰⁴⁸⁰/₈₈ = 460

Thus, the Cost Price (CP) = $460

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

Here now, CP = $460

And, profit = 11%

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 + 11}/₁₀₀ × 460

= ¹¹¹/₁₀₀ × 460

= ^{111 × 460}/₁₀₀

= ⁵¹⁰⁶⁰/₁₀₀ = 510.6

Thus, Sale Price (SP) at a profit of 11% = $510.6 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) = $404.8

And, the loss = 12%

Then, the Sale Price (SP) to earn a profit of 11% = ?

Let the Cost Price (CP) = m

Here given loss = 12%

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

= 12% of m

= 12% × m

= ¹²/₁₀₀ × m

⇒ loss = ^{12 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 404.8 = m – ^{12 m}/₁₀₀

⇒ 404.8 = ^{100 m – 12 m}/₁₀₀

⇒ 404.8 = ^{88 m}/₁₀₀

After cross multiplication, we get

404.8 × 100 = 88 m

⇒ 88 m = 404.8 × 100

⇒ m = ^{404.8 × 100}/₈₈

⇒ m = ⁴⁰⁴⁸⁰/₈₈ = 460

⇒ m = 460

Thus, the Cost Price (CP) = $460

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

Now, here, Cost Price = 460

And, the profit = 11%

Thus, Sale Price (SP)

= Cost Price (CP) + 11% of Cost Price (CP)

= 460 + ¹¹/₁₀₀ × 460

= 460 + ^{11 × 460}/₁₀₀

= 460 + ⁵⁰⁶⁰/₁₀₀

= 460 + 50.6 = 510.6

Thus, Sale Price (SP) at a profit of 11% = $510.6 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) = $404.8

And, the loss = 12%

Then, the Sale Price (SP) to earn a profit of 11% = ?

Let, CP = 100

11% profit = 11% of CP

= 11% of 100 = 11

Thus, Sale Price to earn a profit of 11% = CP + 11

= 100 + 11 = 111

⇒ Sale Price to earn a profit of 11% = 111

12% loss = 12% of CP

= 12% of 100 = 12

Thus, Sale Price at a loss of 12% = CP – Loss

= 100 – 12 = 88

⇒ Sale Price at a loss of 12% = 88

∵ If the Sale Price is 88, then to earn a profit of 11% the Sale Price should be = 111

∴ If the Sale Price is 1, then to earn a profit of 11% the Sale Price should be

= ¹¹¹/₈₈

∴ If the Sale Price is 404.8, then to earn a profit of 11% the Sale Price should be

= ¹¹¹/₈₈ × 404.8

= ^{111 × 404.8}/₈₈

= ^44932.8/₈₈ = 510.6

Thus, Sale Price to get a profit of 11% = $510.6 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) = $404.8

And, the loss = 12%

Then, the Sale Price (SP) to earn a profit of 11% = ?

Here, the Sale Price at a loss of 12 = $404.8

This means 88% of the Cost Price (CP) = 404.8

Therefore, 1% of the Cost Price (CP) = ^404.8/₈₈

Therefore, 100% of the Cost Price (CP)

= ^404.8/₈₈ × 100 = 460

Thus, the Cost Price (CP) = $460

Now, we need to find the Sale Price at a profit of 11%

Thus, Sale Price at a profit of 11%

= 111% of the Cost Price (CP)

= 111% of 460

= ¹¹¹/₁₀₀ × 460 = 510.6

Thus, the Cost Price at a profit of 11% = $510.6 Answer

Similar Questions

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