Profit And Loss
Math MCQs

Question :    If a dealer gets a loss of 75% by selling 200 boxes of apple for $3702.50 then find the cost price.

Correct Answer  $14810

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) = $3702.5

And, the loss = 75%

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 – 75} × 3702.5

= ¹⁰⁰/₂₅ × 3702.5

= ³⁷⁰²⁵⁰/₂₅ = 14810

Thus, the Cost Price (CP) = $14810 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 = 75%

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

= 75% of m

= 75% × m

= ⁷⁵/₁₀₀ × m

⇒ loss = ^{75 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

⇒ 3702.5 = m – ^{75 m}/₁₀₀

⇒ 3702.5 = ^{100 m – 75 m}/₁₀₀

⇒ 3702.5 = ^{25 m}/₁₀₀

After cross multiplication, we get

3702.5 × 100 = 25 m

⇒ 25 m = 3702.5 × 100

⇒ m = ^{3702.5 × 100}/₂₅

⇒ m = ^{3702.5 × 100}/₂₅

⇒ m = ³⁷⁰²⁵⁰/₂₅ = 14810

Thus, the Cost Price (CP) = $14810 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) = $3702.5

And, the loss = 75%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 75% of 100 = 75

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

⇒ Sale Price (SP) = 100 – 75

⇒ Sale Price (SP) = 25

∵ If the Sale Price (SP) is 25, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₂₅

∴ If the Sale Price (SP) is 3702.5, then the Cost Price (CP)

= ¹⁰⁰/₂₅ × 3702.5

= ^{100 × 3702.5}/₂₅ = 14810

Thus, the Cost Price (CP) = $14810 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) = $3702.5

And, the loss = 75%

Then, the Cost Price (CP) = ?

SP = 25% of CP

⇒ SP = 25% of CP

⇒ 3702.5 = ²⁵/₁₀₀ × CP

⇒ 3702.5 = ^{25 CP}/₁₀₀

After cross multiplication

⇒ 3702.5 × 100 = 25 CP

⇒ 25 CP = 3702.5 × 100

⇒ CP = ^{3702.5 × 100}/₂₅

⇒ CP = ³⁷⁰²⁵⁰/₂₅ = 14810

⇒ CP = $14810 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 = 75%

And the Sale Price = $3702.5

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

⇒ 100 – 75% of the Cost Price = $3702.5

⇒ 25% of the Cost Price = 3702.5

Therefore, 1% of the Cost Price = ^3702.5/₂₅

Thus, 100% the Cost Price = ^3702.5/₂₅ × 100

= ³⁷⁰²⁵⁰/₂₅ = 14810

Thus the Cost Price (CP) = $14810 Answer

Similar Questions

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(2) After selling an article for $1565.5 the shopkeeper earns a profit of 55%. For how much had he purchase that article?

(3) Find the cost price, if Mr. Jojo earns a profit of 355% by selling some articles for $31895.5

(4) By selling some items for $1788.90 a vendor gets a loss of 11%. Find the cost price of those items.

(5) Mr. Razor loses 45% by selling an article for $1160.50. For how much should he sell it to get a profit of 44%?

(6) A dealer earns a profit of 285% by selling some items for $21598.50. What was his cost price?

(7) Mrs. Mary earns a profit of 230% after selling an article for $14883. Find the cost price.

(8) 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?

(9) If Mrs. Julie earned a profit of 335% by selling her car for $28753.50 then, what was the cost price of the car?

(10) Mr. Noah loses 37% by selling an article for $1077.30. For how much should he sell it to get a profit of 36%?