Profit And Loss
Math MCQs

Question :    Find the cost price, if a trader gets a loss of 50% by selling 500 bags of rice for $4905

Correct Answer  $9810

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) = $4905

And, the loss = 50%

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 – 50} × 4905

= ¹⁰⁰/₅₀ × 4905

= ⁴⁹⁰⁵⁰⁰/₅₀ = 9810

Thus, the Cost Price (CP) = $9810 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 = 50%

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

= 50% of m

= 50% × m

= ⁵⁰/₁₀₀ × m

⇒ loss = ^{50 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

⇒ 4905 = m – ^{50 m}/₁₀₀

⇒ 4905 = ^{100 m – 50 m}/₁₀₀

⇒ 4905 = ^{50 m}/₁₀₀

After cross multiplication, we get

4905 × 100 = 50 m

⇒ 50 m = 4905 × 100

⇒ m = ^{4905 × 100}/₅₀

⇒ m = ^{4905 × 100}/₅₀

⇒ m = ⁴⁹⁰⁵⁰⁰/₅₀ = 9810

Thus, the Cost Price (CP) = $9810 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) = $4905

And, the loss = 50%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 50% of 100 = 50

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

⇒ Sale Price (SP) = 100 – 50

⇒ Sale Price (SP) = 50

∵ If the Sale Price (SP) is 50, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₅₀

∴ If the Sale Price (SP) is 4905, then the Cost Price (CP)

= ¹⁰⁰/₅₀ × 4905

= ^{100 × 4905}/₅₀ = 9810

Thus, the Cost Price (CP) = $9810 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) = $4905

And, the loss = 50%

Then, the Cost Price (CP) = ?

SP = 50% of CP

⇒ SP = 50% of CP

⇒ 4905 = ⁵⁰/₁₀₀ × CP

⇒ 4905 = ^{50 CP}/₁₀₀

After cross multiplication

⇒ 4905 × 100 = 50 CP

⇒ 50 CP = 4905 × 100

⇒ CP = ^{4905 × 100}/₅₀

⇒ CP = ⁴⁹⁰⁵⁰⁰/₅₀ = 9810

⇒ CP = $9810 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 = 50%

And the Sale Price = $4905

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

⇒ 100 – 50% of the Cost Price = $4905

⇒ 50% of the Cost Price = 4905

Therefore, 1% of the Cost Price = ⁴⁹⁰⁵/₅₀

Thus, 100% the Cost Price = ⁴⁹⁰⁵/₅₀ × 100

= ⁴⁹⁰⁵⁰⁰/₅₀ = 9810

Thus the Cost Price (CP) = $9810 Answer

Similar Questions

(1) A dealer loses 21% by selling an article for $718.90. For how much should he sell it to get a profit of 20%?

(2) A trader loses 30% by selling an article for $952. For how much should he sell it to get a profit of 29%?

(3) A dealer loses 57% by selling an article for $1165.30. For how much should he sell it to get a profit of 56%?

(4) Mike sold his car at a profit of 25%. If he purchased that car at $2500 then find the sale price of the car.

(5) A trader gets a loss of 52% by selling 500 bags of rice for $4900.80. Find the cost price of rice.

(6) John loses 63% by selling an article for $1113.70. For how much should he sell it to get a profit of 62%?

(7) Find the cost price, if a trader gets a loss of 68% by selling five bags of rice for $4291.20

(8) After selling some antique items for $6504 a trader earns a profit of 140%. Find the cost price of those antique items.

(9) Find the profit percent if Mrs. Julie buys 29 bananas for $1 and sells 28 bananas for $1.

(10) A trader loses 54% by selling an article for $1177.60. For how much should he sell it to get a profit of 53%?