Profit And Loss
Math MCQs

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

Correct Answer  $10210

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) = $4900.8

And, the loss = 52%

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 – 52} × 4900.8

= ¹⁰⁰/₄₈ × 4900.8

= ⁴⁹⁰⁰⁸⁰/₄₈ = 10210

Thus, the Cost Price (CP) = $10210 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 = 52%

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

= 52% of m

= 52% × m

= ⁵²/₁₀₀ × m

⇒ loss = ^{52 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

⇒ 4900.8 = m – ^{52 m}/₁₀₀

⇒ 4900.8 = ^{100 m – 52 m}/₁₀₀

⇒ 4900.8 = ^{48 m}/₁₀₀

After cross multiplication, we get

4900.8 × 100 = 48 m

⇒ 48 m = 4900.8 × 100

⇒ m = ^{4900.8 × 100}/₄₈

⇒ m = ^{4900.8 × 100}/₄₈

⇒ m = ⁴⁹⁰⁰⁸⁰/₄₈ = 10210

Thus, the Cost Price (CP) = $10210 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) = $4900.8

And, the loss = 52%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 52% of 100 = 52

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

⇒ Sale Price (SP) = 100 – 52

⇒ Sale Price (SP) = 48

∵ If the Sale Price (SP) is 48, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₄₈

∴ If the Sale Price (SP) is 4900.8, then the Cost Price (CP)

= ¹⁰⁰/₄₈ × 4900.8

= ^{100 × 4900.8}/₄₈ = 10210

Thus, the Cost Price (CP) = $10210 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) = $4900.8

And, the loss = 52%

Then, the Cost Price (CP) = ?

SP = 48% of CP

⇒ SP = 48% of CP

⇒ 4900.8 = ⁴⁸/₁₀₀ × CP

⇒ 4900.8 = ^{48 CP}/₁₀₀

After cross multiplication

⇒ 4900.8 × 100 = 48 CP

⇒ 48 CP = 4900.8 × 100

⇒ CP = ^{4900.8 × 100}/₄₈

⇒ CP = ⁴⁹⁰⁰⁸⁰/₄₈ = 10210

⇒ CP = $10210 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 = 52%

And the Sale Price = $4900.8

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

⇒ 100 – 52% of the Cost Price = $4900.8

⇒ 48% of the Cost Price = 4900.8

Therefore, 1% of the Cost Price = ^4900.8/₄₈

Thus, 100% the Cost Price = ^4900.8/₄₈ × 100

= ⁴⁹⁰⁰⁸⁰/₄₈ = 10210

Thus the Cost Price (CP) = $10210 Answer

Similar Questions

(1) If Mrs. Julie earned a profit of 335% by selling her car for $28753.50 then, what was the cost price of the car?

(2) A dealer loses 60% by selling an article for $1144.00. For how much should he sell it to get a profit of 59%?

(3) Peter loses 3% by selling an article for $9.70. For how much should he sell it to get a profit of 2%?

(4) If a vendor bought 20 apples per $1 and sold them at a rate of 19 apples per $1, then what would his profit percent be?

(5) Mrs. Mary earns a profit of 230% after selling an article for $14883. Find the cost price.

(6) What will the earnings in percent if a vendor buys 42 apples for $1 and sells at a rate of 41 apples per $1?

(7) Noah loses 78% by selling an article for $827.20. For how much should he sell it to get a profit of 77%?

(8) Mr. Steven loses 95% by selling an article for $230.50. For how much should he sell it to get a profit of 94%?

(9) If a seller bought 24 apples per $1 and sold them at a rate of 23 apples per $1, then what would his profit percent be?

(10) Calculate the earnings percentage if a vendor buys 55 articles for $1 and sells 54 articles for $1.