Profit And Loss
Math MCQs

Question :    After selling an article for $1565.5 the shopkeeper earns a profit of 55%. For how much had he purchase that article?

Correct Answer  1010

Solution & Explanation

Solution

Finding the cost price if the sale price and profit percent are known

The cost price (CP) can be found using the formula, algebraic method, using shortcut method, and taking the cost price as 100, 200, 300, 400, 500, or whatever you want.

Finding the cost price using the formula when the sale price and profit percent are known

Given, the sale price (SP) = $1565.5

And, the profit = 55%

Then, the Cost Price (CP) = ?

Formula to find the cost price when the sale price and profit percent are known

Cost Price (CP) = ¹⁰⁰/_{100 + gain%} × SP

Thus, the Cost Price (CP)

= ¹⁰⁰/_{100 + 55} × 1565.5

= ^{100 × 1565.5}/₁₅₅

= ¹⁵⁶⁵⁵⁰/₁₅₅ = 1010

Thus, the Cost Price (CP) = $1010 Answer

Finding the cost price (CP) using the Algebraic Method when the Sale Pric (SP) and the profit percent are given

Let the Cost Price (CP) = m

Here given profit = 55%

Calculation of Profit

Profit is calculated on cost price (CP)

Formula to find the Profit = Profit% of CP

Thus, profit on the cost price of m

= 55% of m

= 55% × m

= ⁵⁵/₁₀₀ × m

⇒ Profit = ^{55 m}/₁₀₀

Calculation of Cost Price (CP)

The Sale Price (SP) = Cost Price (CP) + Profit

⇒ 1565.5 = m + ^{55 m}/₁₀₀

⇒ 1565.5 = ^{100 m + 55 m}/₁₀₀

⇒ 1565.5 = ^{155 m}/₁₀₀

After cross multiplication, we get

1565.5 × 100 = 155 m

⇒ 155 m = 1565.5 × 100

⇒ m = ^{1565.5 × 100}/₁₅₅

⇒ m = ¹⁵⁶⁵⁵⁰/₁₅₅ = 1010

⇒ m = 1010

Thus, the Cost Price (CP) = $1010 Answer

Finding the cost price (CP) using Unitary Method by taking the cost price (CP) is equal to 100 when the SP and the profit percent are given

Given, the sale price (SP) = $1565.5

And, the profit = 55%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 55% of 100 = 55

Thus, Sale Price (SP) = Cost Price (CP) + Profit

⇒ Sale Price (SP) = 100 + 55

⇒ Sale Price (SP) = 155

∵ If the Sale Price (SP) is 155, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₁₅₅

∴ If the Sale Price (SP) is 1565.5, then the Cost Price (CP)

= ¹⁰⁰/₁₅₅ × 1565.5

= ^{100 × 1565.5}/₁₅₅

= ¹⁵⁶⁵⁵⁰/₁₅₅ = 1010

Thus, the Cost Price (CP) = $1010 Answer

Shortcut Method to find Cost Price (CP) when SP and profit percent are known

Given, the sale price (SP) = $1565.5

And, the profit = 55%

Then, the Cost Price (CP) = ?

SP = 155% of CP

⇒ SP = ¹⁵⁵/₁₀₀ × CP

⇒ 1565.5 = ^{155 CP}/₁₀₀

After cross multiplication

⇒ 1565.5 × 100 = 155 CP

⇒ 155 CP = 1565.5 × 100

⇒ CP = ^{1565.5 × 100}/₁₅₅

⇒ CP = ¹⁵⁶⁵⁵⁰/₁₅₅ = 1010

⇒ CP = $1010 Answer

Similar Questions

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

(2) Find the cost price, if a trader gets a loss of 58% by selling two TV sets for $4792.20

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

(4) By selling an article for $1125.30 a vendor gets a loss of 7%. Calculate the cost price.

(5) By selling some items for $1788.90 a vendor gets a loss of 11%. Find the cost price of those items.

(6) Find the cost price, if a broker earns a profit of 385% by selling an article for $36908.5

(7) John sold rice at $7.20 per kg. If he purchased 120 kg of rice for $960, then calculate the loss and loss percent in this sale.

(8) Jojo loses 36% by selling an article for $1062.40. For how much should he sell it to get a profit of 35%?

(9) Noah loses 77% by selling an article for $853.30. For how much should he sell it to get a profit of 76%?

(10) If a dealer earns a profit of 255% by selling some articles for $17785.50, then find the cost price.