Profit And Loss
Math MCQs

Question :    If a shopkeeper gets a loss of 65% by selling five TV sets for $4483.50 then find the cost price of all those TV sets.

Correct Answer  $12810

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) = $4483.5

And, the loss = 65%

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 – 65} × 4483.5

= ¹⁰⁰/₃₅ × 4483.5

= ⁴⁴⁸³⁵⁰/₃₅ = 12810

Thus, the Cost Price (CP) = $12810 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 = 65%

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

= 65% of m

= 65% × m

= ⁶⁵/₁₀₀ × m

⇒ loss = ^{65 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

⇒ 4483.5 = m – ^{65 m}/₁₀₀

⇒ 4483.5 = ^{100 m – 65 m}/₁₀₀

⇒ 4483.5 = ^{35 m}/₁₀₀

After cross multiplication, we get

4483.5 × 100 = 35 m

⇒ 35 m = 4483.5 × 100

⇒ m = ^{4483.5 × 100}/₃₅

⇒ m = ^{4483.5 × 100}/₃₅

⇒ m = ⁴⁴⁸³⁵⁰/₃₅ = 12810

Thus, the Cost Price (CP) = $12810 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) = $4483.5

And, the loss = 65%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 65% of 100 = 65

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

⇒ Sale Price (SP) = 100 – 65

⇒ Sale Price (SP) = 35

∵ If the Sale Price (SP) is 35, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₃₅

∴ If the Sale Price (SP) is 4483.5, then the Cost Price (CP)

= ¹⁰⁰/₃₅ × 4483.5

= ^{100 × 4483.5}/₃₅ = 12810

Thus, the Cost Price (CP) = $12810 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) = $4483.5

And, the loss = 65%

Then, the Cost Price (CP) = ?

SP = 35% of CP

⇒ SP = 35% of CP

⇒ 4483.5 = ³⁵/₁₀₀ × CP

⇒ 4483.5 = ^{35 CP}/₁₀₀

After cross multiplication

⇒ 4483.5 × 100 = 35 CP

⇒ 35 CP = 4483.5 × 100

⇒ CP = ^{4483.5 × 100}/₃₅

⇒ CP = ⁴⁴⁸³⁵⁰/₃₅ = 12810

⇒ CP = $12810 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 = 65%

And the Sale Price = $4483.5

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

⇒ 100 – 65% of the Cost Price = $4483.5

⇒ 35% of the Cost Price = 4483.5

Therefore, 1% of the Cost Price = ^4483.5/₃₅

Thus, 100% the Cost Price = ^4483.5/₃₅ × 100

= ⁴⁴⁸³⁵⁰/₃₅ = 12810

Thus the Cost Price (CP) = $12810 Answer

Similar Questions

(1) Find the cost price, if a trader gets a loss of 63% by selling 15 TV sets for $4591.7

(2) If after selling 5 bags of rice for $1297.20 a shopkeeper gets a loss of 8% then what was the cost price of the rice?

(3) Find the cost price, if a trader gets a loss of 44% by selling 500 packets of fruits for $48210.60

(4) By selling an article for $15443.50, Mrs. Linda earns a profit of 235%. What was the cost price?

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

(6) A dealer earns a profit of 285% by selling some items for $21598.50. What was his cost price?

(7) Mr. James gets a profit of 180% by selling a plot for $9828. Find the cost price of that plot.

(8) Mr. Oliver loses 34% by selling an article for $1029.60. For how much should he sell it to get a profit of 33%?

(9) Find the cost price, if a shopkeeper earns a profit of 300% by selling some articles for $23640

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