Profit And Loss
Math MCQs

Question :    What will be the cost price, if a trader gets a loss of 2% by selling an article for $205.80?

Correct Answer  $210

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) = $205.8

And, the loss = 2%

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 – 2} × 205.8

= ¹⁰⁰/₉₈ × 205.8

= ²⁰⁵⁸⁰/₉₈ = 210

Thus, the Cost Price (CP) = $210 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 = 2%

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

= 2% of m

= 2% × m

= ²/₁₀₀ × m

⇒ loss = ^{2 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

⇒ 205.8 = m – ^{2 m}/₁₀₀

⇒ 205.8 = ^{100 m – 2 m}/₁₀₀

⇒ 205.8 = ^{98 m}/₁₀₀

After cross multiplication, we get

205.8 × 100 = 98 m

⇒ 98 m = 205.8 × 100

⇒ m = ^{205.8 × 100}/₉₈

⇒ m = ^{205.8 × 100}/₉₈

⇒ m = ²⁰⁵⁸⁰/₉₈ = 210

Thus, the Cost Price (CP) = $210 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) = $205.8

And, the loss = 2%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 2% of 100 = 2

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

⇒ Sale Price (SP) = 100 – 2

⇒ Sale Price (SP) = 98

∵ If the Sale Price (SP) is 98, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₉₈

∴ If the Sale Price (SP) is 205.8, then the Cost Price (CP)

= ¹⁰⁰/₉₈ × 205.8

= ^{100 × 205.8}/₉₈ = 210

Thus, the Cost Price (CP) = $210 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) = $205.8

And, the loss = 2%

Then, the Cost Price (CP) = ?

SP = 98% of CP

⇒ SP = 98% of CP

⇒ 205.8 = ⁹⁸/₁₀₀ × CP

⇒ 205.8 = ^{98 CP}/₁₀₀

After cross multiplication

⇒ 205.8 × 100 = 98 CP

⇒ 98 CP = 205.8 × 100

⇒ CP = ^{205.8 × 100}/₉₈

⇒ CP = ²⁰⁵⁸⁰/₉₈ = 210

⇒ CP = $210 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 = 2%

And the Sale Price = $205.8

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

⇒ 100 – 2% of the Cost Price = $205.8

⇒ 98% of the Cost Price = 205.8

Therefore, 1% of the Cost Price = ^205.8/₉₈

Thus, 100% the Cost Price = ^205.8/₉₈ × 100

= ²⁰⁵⁸⁰/₉₈ = 210

Thus the Cost Price (CP) = $210 Answer

Similar Questions

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(2) A shopkeeper loses 51% by selling an article for $1180.90. For how much should he sell it to get a profit of 50%?

(3) If Rohilla sold his furniture for $663 at a profit of 30%, then for how much he had purchased them?

(4) After selling some articles for $13261.50, a trader earns a profit of 215%. Find the cost price.

(5) Mr. Peter earns a profit of 110% by selling goods for $4431.00. For how much was he purchased those goods?

(6) James loses 65% by selling an article for $1088.50. For how much should he sell it to get a profit of 64%?

(7) A peddler purchased 25 apples per $1 and sold them at a rate of 24 apples per $1. What will be the profit percent?

(8) If Mr. Peter buys 17 apples for $1 and sells 16 apples for $1 then, find the profit percent in this sale.

(9) By selling some antique items for $20938 Mr. David earns a profit of 280%. Find the cost price.

(10) A trader loses 47% by selling an article for $1171.30. For how much should he sell it to get a profit of 46%?