Profit And Loss
Math MCQs

Question :    By selling an article for $1125.30 a vendor gets a loss of 7%. Calculate the cost price.

Correct Answer  $1210

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) = $1125.3

And, the loss = 7%

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 – 7} × 1125.3

= ¹⁰⁰/₉₃ × 1125.3

= ¹¹²⁵³⁰/₉₃ = 1210

Thus, the Cost Price (CP) = $1210 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 = 7%

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

= 7% of m

= 7% × m

= ²/₁₀₀ × m

⇒ loss = ^{7 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

⇒ 1125.3 = m – ^{7 m}/₁₀₀

⇒ 1125.3 = ^{100 m – 7 m}/₁₀₀

⇒ 1125.3 = ^{93 m}/₁₀₀

After cross multiplication, we get

1125.3 × 100 = 93 m

⇒ 93 m = 1125.3 × 100

⇒ m = ^{1125.3 × 100}/₉₃

⇒ m = ^{1125.3 × 100}/₉₃

⇒ m = ¹¹²⁵³⁰/₉₃ = 1210

Thus, the Cost Price (CP) = $1210 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) = $1125.3

And, the loss = 7%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 7% of 100 = 7

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

⇒ Sale Price (SP) = 100 – 7

⇒ Sale Price (SP) = 93

∵ If the Sale Price (SP) is 93, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₉₃

∴ If the Sale Price (SP) is 1125.3, then the Cost Price (CP)

= ¹⁰⁰/₉₃ × 1125.3

= ^{100 × 1125.3}/₉₃ = 1210

Thus, the Cost Price (CP) = $1210 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) = $1125.3

And, the loss = 7%

Then, the Cost Price (CP) = ?

SP = 93% of CP

⇒ SP = 93% of CP

⇒ 1125.3 = ⁹³/₁₀₀ × CP

⇒ 1125.3 = ^{93 CP}/₁₀₀

After cross multiplication

⇒ 1125.3 × 100 = 93 CP

⇒ 93 CP = 1125.3 × 100

⇒ CP = ^{1125.3 × 100}/₉₃

⇒ CP = ¹¹²⁵³⁰/₉₃ = 1210

⇒ CP = $1210 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 = 7%

And the Sale Price = $1125.3

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

⇒ 100 – 7% of the Cost Price = $1125.3

⇒ 93% of the Cost Price = 1125.3

Therefore, 1% of the Cost Price = ^1125.3/₉₃

Thus, 100% the Cost Price = ^1125.3/₉₃ × 100

= ¹¹²⁵³⁰/₉₃ = 1210

Thus the Cost Price (CP) = $1210 Answer

Similar Questions

(1) William loses 75% by selling an article for $902.50. For how much should he sell it to get a profit of 74%?

(2) If a vendor bought 20 apples per $1 and sold them at a rate of 19 apples per $1, then what would his profit percent be?

(3) A shopkeeper earns 130% after selling some old bikes for $5773. What was his cost price?

(4) A dealer loses 23% by selling an article for $777.7. For how much should he sell it to get a profit of 22%?

(5) What will be the cost price if a shopkeeper sells some clothes for $994 and earns a profit of 40%?

(6) Mrs. Jolly loses 18% by selling an article for $623.20. For how much should she sell it to get a profit of 17%?

(7) Find the cost price, if Mrs. Mary earns a profit of 270% by selling some articles for $19647

(8) Find the cost price, if a trader gets a loss of 38% by selling 600 packets of fruits for $4594.20

(9) Mr. Bob buys 40 articles for $1 and sells 39 articles for $1. Find the profit percent in this sale.

(10) Calculate the earnings percentage if a vendor buys 56 articles for $1 and sells 55 articles for $1.