Profit And Loss
Math MCQs

Question :    Find the cost price, if a vendor gets a loss of 15% by selling some articles for $2388.50.

Correct Answer  $2810

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) = $2388.5

And, the loss = 15%

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 – 15} × 2388.5

= ¹⁰⁰/₈₅ × 2388.5

= ²³⁸⁸⁵⁰/₈₅ = 2810

Thus, the Cost Price (CP) = $2810 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 = 15%

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

= 15% of m

= 15% × m

= ²/₁₀₀ × m

⇒ loss = ^{15 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

⇒ 2388.5 = m – ^{15 m}/₁₀₀

⇒ 2388.5 = ^{100 m – 15 m}/₁₀₀

⇒ 2388.5 = ^{85 m}/₁₀₀

After cross multiplication, we get

2388.5 × 100 = 85 m

⇒ 85 m = 2388.5 × 100

⇒ m = ^{2388.5 × 100}/₈₅

⇒ m = ^{2388.5 × 100}/₈₅

⇒ m = ²³⁸⁸⁵⁰/₈₅ = 2810

Thus, the Cost Price (CP) = $2810 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) = $2388.5

And, the loss = 15%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 15% of 100 = 15

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

⇒ Sale Price (SP) = 100 – 15

⇒ Sale Price (SP) = 85

∵ If the Sale Price (SP) is 85, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₈₅

∴ If the Sale Price (SP) is 2388.5, then the Cost Price (CP)

= ¹⁰⁰/₈₅ × 2388.5

= ^{100 × 2388.5}/₈₅ = 2810

Thus, the Cost Price (CP) = $2810 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) = $2388.5

And, the loss = 15%

Then, the Cost Price (CP) = ?

SP = 85% of CP

⇒ SP = 85% of CP

⇒ 2388.5 = ⁸⁵/₁₀₀ × CP

⇒ 2388.5 = ^{85 CP}/₁₀₀

After cross multiplication

⇒ 2388.5 × 100 = 85 CP

⇒ 85 CP = 2388.5 × 100

⇒ CP = ^{2388.5 × 100}/₈₅

⇒ CP = ²³⁸⁸⁵⁰/₈₅ = 2810

⇒ CP = $2810 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 = 15%

And the Sale Price = $2388.5

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

⇒ 100 – 15% of the Cost Price = $2388.5

⇒ 85% of the Cost Price = 2388.5

Therefore, 1% of the Cost Price = ^2388.5/₈₅

Thus, 100% the Cost Price = ^2388.5/₈₅ × 100

= ²³⁸⁸⁵⁰/₈₅ = 2810

Thus the Cost Price (CP) = $2810 Answer

Similar Questions

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(2) Find the cost price, if a trader gets a loss of 48% by selling 500 kg of rice for $4893.20

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

(4) Find the cost price, if a dealer earns a profit of 345% by selling some goods for $30304.5

(5) A trader loses 52% by selling an article for $1180.80. For how much should he sell it to get a profit of 51%?

(6) Mr. William buys 15 toffees for $1 and sells 14 tofees for $1. What is the profit percent?

(7) If Mr. Jobby buys 18 kiwis for $1 and sells them at a rate of 17 per $1 then what would be the profit percent?.

(8) William loses 43% by selling an article for $1145.70. For how much should he sell it to get a profit of 42%?

(9) A shopkeeper earns a profit of 50% by selling an article for $1365. Find the cost price of the article.

(10) John purchased a bike for $500 and he sold it at a gain of 12%. Find the sale price of the bike.