Profit And Loss
Math MCQs

Question :    If a book seller gets a loss of 33% by selling 300 books for $4294.70 then find the cost price of the books.

Correct Answer  $6410

Solution & Explanation

Solution

Finding the cost price if the sale price and loss percent are known

The cost price (CP) can be found using the formula, algebraic method, shortcut method, and taking the cost price as 100, 200, 300, 400, 500, or whatever you want. Here the five methods to solve this problem have been given.

Method (1) Using Formula

Finding the cost price using the formula when the sale price and loss percent are known

Given, the sale price (SP) = $4294.7

And, the loss = 33%

Then, the Cost Price (CP) = ?

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 – 33} × 4294.7

= ¹⁰⁰/₆₇ × 4294.7

= ⁴²⁹⁴⁷⁰/₆₇ = 6410

Thus, the Cost Price (CP) = $6410 Answer

Method (2) Algebraic Method

Finding the cost price (CP) using the Algebraic Method when the Sale Price (SP) and the loss percent are given

Let the Cost Price (CP) = m

Here given loss = 33%

Calculation of loss

The loss and/or profit is calculated on the cost price (CP)

Formula to find the loss when the Cost Price and the Loss% are given

Loss = loss% of CP

Thus, loss on the cost price of m

= Loss% of m

= 33% of m

= 33% × m

= ²/₁₀₀ × m

⇒ loss = ^{33 m}/₁₀₀

Calculation of Cost Price (CP)

Formula to find the Sale Price (SP) when the Cost Price (CP) and the Loss are given

Sale Price (SP) = Cost Price (CP) – Loss

⇒ 4294.7 = m – ^{33 m}/₁₀₀

⇒ 4294.7 = ^{100 m – 33 m}/₁₀₀

⇒ 4294.7 = ^{67 m}/₁₀₀

After cross multiplication, we get

4294.7 × 100 = 67 m

⇒ 67 m = 4294.7 × 100

⇒ m = ^{4294.7 × 100}/₆₇

⇒ m = ^{4294.7 × 100}/₆₇

⇒ m = ⁴²⁹⁴⁷⁰/₆₇ = 6410

Thus, the Cost Price (CP) = $6410 Answer

Method (3) Unitary Method

Finding the cost price (CP) using Unitary Method by taking the cost price (CP) is equal to 100 when the SP and the loss percent are given

Given, the sale price (SP) = $4294.7

And, the loss = 33%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 33% of 100 = 33

Thus, Sale Price (SP) = Cost Price (CP) – loss

⇒ Sale Price (SP) = 100 – 33

⇒ Sale Price (SP) = 67

∵ If the Sale Price (SP) is 67, then the Cost Price (CP) = 100

∴ If the Sale Price (SP) is 1, then the Cost Price (CP)

= ¹⁰⁰/₆₇

∴ If the Sale Price (SP) is 4294.7, then the Cost Price (CP)

= ¹⁰⁰/₆₇ × 4294.7

= ^{100 × 4294.7}/₆₇ = 6410

Thus, the Cost Price (CP) = $6410 Answer

Method (4) Shortcut Method (1)

Shortcut Method to find Cost Price (CP) when SP and loss percent are known

Given, the sale price (SP) = $4294.7

And, the loss = 33%

Then, the Cost Price (CP) = ?

SP = 67% of CP

⇒ SP = 67% of CP

⇒ 4294.7 = ⁶⁷/₁₀₀ × CP

⇒ 4294.7 = ^{67 CP}/₁₀₀

After cross multiplication

⇒ 4294.7 × 100 = 67 CP

⇒ 67 CP = 4294.7 × 100

⇒ CP = ^{4294.7 × 100}/₆₇

⇒ CP = ⁴²⁹⁴⁷⁰/₆₇ = 6410

⇒ CP = $6410 Answer

Method (5) Shortcut Method (2)

Shortcut Method (2) to find Cost Price (CP) when SP and loss percent are known

Here loss and the Sale Price are given and the Cost Price is to find

Here as given, the loss = 33%

And the Sale Price = $4294.7

This means 100 – loss% of the Cost Price = Sale Price

⇒ 100 – 33% of the Cost Price = $4294.7

⇒ 67% of the Cost Price = 4294.7

Therefore, 1% of the Cost Price = ^4294.7/₆₇

Thus, 100% the Cost Price = ^4294.7/₆₇ × 100

= ⁴²⁹⁴⁷⁰/₆₇ = 6410

Thus the Cost Price (CP) = $6410 Answer

Similar Questions

(1) Mr. Robert sold his motorcycle for $1629 and got a loss of 10%. What was his cost price?

(2) William loses 69% by selling an article for $1026.10. For how much should he sell it to get a profit of 68%?

(3) After selling some antique items for $6504 a trader earns a profit of 140%. Find the cost price of those antique items.

(4) If a trader gets a loss of 4% by selling an article for $585.60 then, find the cost price.

(5) A dealer loses 21% by selling an article for $718.90. For how much should he sell it to get a profit of 20%?

(6) How much Mr. Gates had to pay to purchase his motorbike? If he gets a profit of 70% after selling it for $2227.

(7) Mr. Bob gets a loss of 11% after selling an article for $364.90. For how much would he sell it to get a profit of 10%?

(8) Mr. Bose loses 98% by selling an article for $95.20. For how much should he sell it to get a profit of 97%?

(9) If a vendor buys 7 lemons for $1 and sells 6 lemons for $1 then, what is the profit percent in this sale?

(10) For how much should he sell it to get a profit of 16%, if Mr. Bond loses 17% by selling a bicycle for $589.30?