Profit And Loss
Math MCQs

Question :    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?

Correct Answer  $1410

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) = $1297.2

And, the loss = 8%

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 – 8} × 1297.2

= ¹⁰⁰/₉₂ × 1297.2

= ¹²⁹⁷²⁰/₉₂ = 1410

Thus, the Cost Price (CP) = $1410 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 = 8%

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

= 8% of m

= 8% × m

= ²/₁₀₀ × m

⇒ loss = ^{8 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

⇒ 1297.2 = m – ^{8 m}/₁₀₀

⇒ 1297.2 = ^{100 m – 8 m}/₁₀₀

⇒ 1297.2 = ^{92 m}/₁₀₀

After cross multiplication, we get

1297.2 × 100 = 92 m

⇒ 92 m = 1297.2 × 100

⇒ m = ^{1297.2 × 100}/₉₂

⇒ m = ^{1297.2 × 100}/₉₂

⇒ m = ¹²⁹⁷²⁰/₉₂ = 1410

Thus, the Cost Price (CP) = $1410 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) = $1297.2

And, the loss = 8%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 8% of 100 = 8

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

⇒ Sale Price (SP) = 100 – 8

⇒ Sale Price (SP) = 92

∵ If the Sale Price (SP) is 92, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₉₂

∴ If the Sale Price (SP) is 1297.2, then the Cost Price (CP)

= ¹⁰⁰/₉₂ × 1297.2

= ^{100 × 1297.2}/₉₂ = 1410

Thus, the Cost Price (CP) = $1410 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) = $1297.2

And, the loss = 8%

Then, the Cost Price (CP) = ?

SP = 92% of CP

⇒ SP = 92% of CP

⇒ 1297.2 = ⁹²/₁₀₀ × CP

⇒ 1297.2 = ^{92 CP}/₁₀₀

After cross multiplication

⇒ 1297.2 × 100 = 92 CP

⇒ 92 CP = 1297.2 × 100

⇒ CP = ^{1297.2 × 100}/₉₂

⇒ CP = ¹²⁹⁷²⁰/₉₂ = 1410

⇒ CP = $1410 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 = 8%

And the Sale Price = $1297.2

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

⇒ 100 – 8% of the Cost Price = $1297.2

⇒ 92% of the Cost Price = 1297.2

Therefore, 1% of the Cost Price = ^1297.2/₉₂

Thus, 100% the Cost Price = ^1297.2/₉₂ × 100

= ¹²⁹⁷²⁰/₉₂ = 1410

Thus the Cost Price (CP) = $1410 Answer

Similar Questions

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(2) A trader loses 47% by selling an article for $1171.30. For how much should he sell it to get a profit of 46%?

(3) Find the cost price, if a trader gets a loss of 36% by selling 500 packets of fruits for $4486.40

(4) If a shopkeeper loses 6% by selling some items for $150.40 then, for how much should he sell them to get a profit of 5%?

(5) Mr. Jack gets a profit of 195% by selling some articles for $11239.50. What was his cost price?

(6) Mr. Donald loses 85% by selling an article for $616.50. For how much should he sell it to get a profit of 84%?

(7) If a trader gets a loss of 20% by selling some apples for $3048, then find the cost price of those apples.

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

(9) 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.

(10) If Robert purchased a TV set in an auction at $250 and sold it at $300, then calculate the profit earned and profit percent in this sale.