Profit And Loss
Math MCQs

Question :    Find the cost price, if a trader gets a loss of 45% by selling 800 bags of fruits for $4845.50

Correct Answer  $8810

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) = $4845.5

And, the loss = 45%

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 – 45} × 4845.5

= ¹⁰⁰/₅₅ × 4845.5

= ⁴⁸⁴⁵⁵⁰/₅₅ = 8810

Thus, the Cost Price (CP) = $8810 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 = 45%

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

= 45% of m

= 45% × m

= ⁴⁵/₁₀₀ × m

⇒ loss = ^{45 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

⇒ 4845.5 = m – ^{45 m}/₁₀₀

⇒ 4845.5 = ^{100 m – 45 m}/₁₀₀

⇒ 4845.5 = ^{55 m}/₁₀₀

After cross multiplication, we get

4845.5 × 100 = 55 m

⇒ 55 m = 4845.5 × 100

⇒ m = ^{4845.5 × 100}/₅₅

⇒ m = ^{4845.5 × 100}/₅₅

⇒ m = ⁴⁸⁴⁵⁵⁰/₅₅ = 8810

Thus, the Cost Price (CP) = $8810 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) = $4845.5

And, the loss = 45%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 45% of 100 = 45

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

⇒ Sale Price (SP) = 100 – 45

⇒ Sale Price (SP) = 55

∵ If the Sale Price (SP) is 55, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₅₅

∴ If the Sale Price (SP) is 4845.5, then the Cost Price (CP)

= ¹⁰⁰/₅₅ × 4845.5

= ^{100 × 4845.5}/₅₅ = 8810

Thus, the Cost Price (CP) = $8810 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) = $4845.5

And, the loss = 45%

Then, the Cost Price (CP) = ?

SP = 55% of CP

⇒ SP = 55% of CP

⇒ 4845.5 = ⁵⁵/₁₀₀ × CP

⇒ 4845.5 = ^{55 CP}/₁₀₀

After cross multiplication

⇒ 4845.5 × 100 = 55 CP

⇒ 55 CP = 4845.5 × 100

⇒ CP = ^{4845.5 × 100}/₅₅

⇒ CP = ⁴⁸⁴⁵⁵⁰/₅₅ = 8810

⇒ CP = $8810 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 = 45%

And the Sale Price = $4845.5

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

⇒ 100 – 45% of the Cost Price = $4845.5

⇒ 55% of the Cost Price = 4845.5

Therefore, 1% of the Cost Price = ^4845.5/₅₅

Thus, 100% the Cost Price = ^4845.5/₅₅ × 100

= ⁴⁸⁴⁵⁵⁰/₅₅ = 8810

Thus the Cost Price (CP) = $8810 Answer

Similar Questions

(1) By selling some items for $12741.00 a trader earns a profit of 210%. Find the cost price.

(2) A trader earns a profit of 95% by selling an article for $3529.50. What was his cost price?

(3) After selling an article for $282.10, a shopkeeper gets a loss of 9%. Thus, to earn a profit of 8% he should sell it at which price?

(4) On a closing day, a shopkeeper earns a profit of 65%. If gets $1996.5 in total, then what was his cost price?

(5) If a trader gets a loss of 71% by selling 150 bags of corn flakes for $4062.90 then find the cost price of the corn flakes.

(6) Mrs. Rosy loses 25% by selling her stock shares for $832.50. For how much should she sell them to get a profit of 24%?

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

(8) By selling some goods for $3249 a shopkeeper earns a profit of 90%. Find the cost price of those goods.

(9) What will be profit percent if a peddler buys 12 kiwis for $1 and sells 11 kiwis for $1?

(10) If a hawker bought 23 apples per $1 and sold them at a rate of 22 apples per $1, then what would his profit percent be?