Profit And Loss
Math MCQs

Question :    What was the cost price, if a trader gets a loss of 18% by selling some articles for $2796.20?

Correct Answer  $3410

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) = $2796.2

And, the loss = 18%

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 – 18} × 2796.2

= ¹⁰⁰/₈₂ × 2796.2

= ²⁷⁹⁶²⁰/₈₂ = 3410

Thus, the Cost Price (CP) = $3410 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 = 18%

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

= 18% of m

= 18% × m

= ²/₁₀₀ × m

⇒ loss = ^{18 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

⇒ 2796.2 = m – ^{18 m}/₁₀₀

⇒ 2796.2 = ^{100 m – 18 m}/₁₀₀

⇒ 2796.2 = ^{82 m}/₁₀₀

After cross multiplication, we get

2796.2 × 100 = 82 m

⇒ 82 m = 2796.2 × 100

⇒ m = ^{2796.2 × 100}/₈₂

⇒ m = ^{2796.2 × 100}/₈₂

⇒ m = ²⁷⁹⁶²⁰/₈₂ = 3410

Thus, the Cost Price (CP) = $3410 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) = $2796.2

And, the loss = 18%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 18% of 100 = 18

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

⇒ Sale Price (SP) = 100 – 18

⇒ Sale Price (SP) = 82

∵ If the Sale Price (SP) is 82, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₈₂

∴ If the Sale Price (SP) is 2796.2, then the Cost Price (CP)

= ¹⁰⁰/₈₂ × 2796.2

= ^{100 × 2796.2}/₈₂ = 3410

Thus, the Cost Price (CP) = $3410 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) = $2796.2

And, the loss = 18%

Then, the Cost Price (CP) = ?

SP = 82% of CP

⇒ SP = 82% of CP

⇒ 2796.2 = ⁸²/₁₀₀ × CP

⇒ 2796.2 = ^{82 CP}/₁₀₀

After cross multiplication

⇒ 2796.2 × 100 = 82 CP

⇒ 82 CP = 2796.2 × 100

⇒ CP = ^{2796.2 × 100}/₈₂

⇒ CP = ²⁷⁹⁶²⁰/₈₂ = 3410

⇒ CP = $3410 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 = 18%

And the Sale Price = $2796.2

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

⇒ 100 – 18% of the Cost Price = $2796.2

⇒ 82% of the Cost Price = 2796.2

Therefore, 1% of the Cost Price = ^2796.2/₈₂

Thus, 100% the Cost Price = ^2796.2/₈₂ × 100

= ²⁷⁹⁶²⁰/₈₂ = 3410

Thus the Cost Price (CP) = $3410 Answer

Similar Questions

(1) Mr. Bose loses 97% by selling an article for $141.30. For how much should he sell it to get a profit of 96%?

(2) What will be thr profit in percent if a vendor purchased 76 pins for $1 and sold 75 pins for $1?

(3) After selling some items for $6884.50 Mr. Bob earns 145%. Find the cost price of those items.

(4) 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?

(5) Bill sold his secondhand motorcycle for $512.50. In this sale, he got a profit of 25%. For how much amount had he purchased the motorcycle?

(6) William loses 73% by selling an article for $947.70. For how much should he sell it to get a profit of 72%?

(7) Mr. Bose loses 98% by selling an article for $95.20. For how much should he sell it to get a profit of 97%?

(8) Find the cost price, if a shopkeeper earns a profit of 240% by selling an article for $16014

(9) If a trader gets a loss of 55% by selling 15 bags of fruits for $4864.50 then find the cost price of fruits.

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