Profit And Loss
Math MCQs

Question :    If a shopkeeper gets a loss of 53% by selling 200 kg of rice for $4892.70 then find the cost price of rice.

Correct Answer  $10410

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) = $4892.7

And, the loss = 53%

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 – 53} × 4892.7

= ¹⁰⁰/₄₇ × 4892.7

= ⁴⁸⁹²⁷⁰/₄₇ = 10410

Thus, the Cost Price (CP) = $10410 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 = 53%

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

= 53% of m

= 53% × m

= ⁵³/₁₀₀ × m

⇒ loss = ^{53 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

⇒ 4892.7 = m – ^{53 m}/₁₀₀

⇒ 4892.7 = ^{100 m – 53 m}/₁₀₀

⇒ 4892.7 = ^{47 m}/₁₀₀

After cross multiplication, we get

4892.7 × 100 = 47 m

⇒ 47 m = 4892.7 × 100

⇒ m = ^{4892.7 × 100}/₄₇

⇒ m = ^{4892.7 × 100}/₄₇

⇒ m = ⁴⁸⁹²⁷⁰/₄₇ = 10410

Thus, the Cost Price (CP) = $10410 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) = $4892.7

And, the loss = 53%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 53% of 100 = 53

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

⇒ Sale Price (SP) = 100 – 53

⇒ Sale Price (SP) = 47

∵ If the Sale Price (SP) is 47, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₄₇

∴ If the Sale Price (SP) is 4892.7, then the Cost Price (CP)

= ¹⁰⁰/₄₇ × 4892.7

= ^{100 × 4892.7}/₄₇ = 10410

Thus, the Cost Price (CP) = $10410 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) = $4892.7

And, the loss = 53%

Then, the Cost Price (CP) = ?

SP = 47% of CP

⇒ SP = 47% of CP

⇒ 4892.7 = ⁴⁷/₁₀₀ × CP

⇒ 4892.7 = ^{47 CP}/₁₀₀

After cross multiplication

⇒ 4892.7 × 100 = 47 CP

⇒ 47 CP = 4892.7 × 100

⇒ CP = ^{4892.7 × 100}/₄₇

⇒ CP = ⁴⁸⁹²⁷⁰/₄₇ = 10410

⇒ CP = $10410 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 = 53%

And the Sale Price = $4892.7

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

⇒ 100 – 53% of the Cost Price = $4892.7

⇒ 47% of the Cost Price = 4892.7

Therefore, 1% of the Cost Price = ^4892.7/₄₇

Thus, 100% the Cost Price = ^4892.7/₄₇ × 100

= ⁴⁸⁹²⁷⁰/₄₇ = 10410

Thus the Cost Price (CP) = $10410 Answer

Similar Questions

(1) Mrs. Julie purchased 27 oranges for $1 and sold 26 oranges for $1. What will be his profit percentage?

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

(3) A shopkeeper loses 22% by selling an article for $748.80. For how much should he sell it to get a profit of 21%?

(4) To earn a profit of 7% Mr. Robert should sell his article for how much if he gets a loss of 8% by selling it for $239.20?

(5) If a trader earns a profit of 10% by selling rice for $121 per kg, then find the cost price of the rice

(6) Find the cost price, if a dealer earns a profit of 245% by selling a plot for $16594.5

(7) Potter loses 91% by selling an article for $396.90. For how much should he sell it to get a profit of 90%?

(8) A trader loses 48% by selling an article for $1175.20. For how much should he sell it to get a profit of 47%?

(9) If a vendor buys 60 articles for $1 and sells 59 articles for $1 then, calculate the profit in percent.

(10) Find the cost price, if a trader gets a loss of 67% by selling ten bags of apple for $4359.30