Profit And Loss
Math MCQs

Question :    Find the cost price, if a trader gets a loss of 60% by selling five TV sets for $4724

Correct Answer  $11810

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) = $4724

And, the loss = 60%

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 – 60} × 4724

= ¹⁰⁰/₄₀ × 4724

= ⁴⁷²⁴⁰⁰/₄₀ = 11810

Thus, the Cost Price (CP) = $11810 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 = 60%

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

= 60% of m

= 60% × m

= ⁶⁰/₁₀₀ × m

⇒ loss = ^{60 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

⇒ 4724 = m – ^{60 m}/₁₀₀

⇒ 4724 = ^{100 m – 60 m}/₁₀₀

⇒ 4724 = ^{40 m}/₁₀₀

After cross multiplication, we get

4724 × 100 = 40 m

⇒ 40 m = 4724 × 100

⇒ m = ^{4724 × 100}/₄₀

⇒ m = ^{4724 × 100}/₄₀

⇒ m = ⁴⁷²⁴⁰⁰/₄₀ = 11810

Thus, the Cost Price (CP) = $11810 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) = $4724

And, the loss = 60%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 60% of 100 = 60

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

⇒ Sale Price (SP) = 100 – 60

⇒ Sale Price (SP) = 40

∵ If the Sale Price (SP) is 40, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₄₀

∴ If the Sale Price (SP) is 4724, then the Cost Price (CP)

= ¹⁰⁰/₄₀ × 4724

= ^{100 × 4724}/₄₀ = 11810

Thus, the Cost Price (CP) = $11810 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) = $4724

And, the loss = 60%

Then, the Cost Price (CP) = ?

SP = 40% of CP

⇒ SP = 40% of CP

⇒ 4724 = ⁴⁰/₁₀₀ × CP

⇒ 4724 = ^{40 CP}/₁₀₀

After cross multiplication

⇒ 4724 × 100 = 40 CP

⇒ 40 CP = 4724 × 100

⇒ CP = ^{4724 × 100}/₄₀

⇒ CP = ⁴⁷²⁴⁰⁰/₄₀ = 11810

⇒ CP = $11810 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 = 60%

And the Sale Price = $4724

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

⇒ 100 – 60% of the Cost Price = $4724

⇒ 40% of the Cost Price = 4724

Therefore, 1% of the Cost Price = ⁴⁷²⁴/₄₀

Thus, 100% the Cost Price = ⁴⁷²⁴/₄₀ × 100

= ⁴⁷²⁴⁰⁰/₄₀ = 11810

Thus the Cost Price (CP) = $11810 Answer

Similar Questions

(1) Find the cost price, if a vendor gets a loss of 34% by selling some articles for $4362.60

(2) Bill sold his bicycle at a profit of 15%. If he purchased that bicycle at $200 then find the sale price of the cycle.

(3) William loses 72% by selling an article for $968.80. For how much should he sell it to get a profit of 71%?

(4) By selling a car for $4751.5 Mr. Aron earns a profit of 115%. For how much was he purchased his car?

(5) For how much should Mr. John sell it to get a profit of 3% if he loses 4% by selling an article for $57.60?

(6) John gets a 20% profit after selling his laptop for $372. What was the cost price of the laptop?

(7) John loses 64% by selling an article for $1101.60. For how much should he sell it to get a profit of 63%?

(8) Find the cost price, if Mrs. Julie earns a profit of 360% by selling some articles for $32706

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

(10) Mrs. John earned a profit of 330% by selling her car. If she sold her car for $27993, then find the cost price of the car.