Profit And Loss
Math MCQs

Question :    What will be the cost price if Peter eans a profit of 15% by selling a scooty for $241.5?

Correct Answer  210

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) = $241.5

And, the profit = 15%

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 + 15} × 241.5

= ^{100 × 241.5}/₁₁₅

= ²⁴¹⁵⁰/₁₁₅ = 210

Thus, the Cost Price (CP) = $210 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 = 15%

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

= 15% of m

= 15% × m

= ¹⁵/₁₀₀ × m

⇒ Profit = ^{15 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 241.5 = m + ^{15 m}/₁₀₀

⇒ 241.5 = ^{100 m + 15 m}/₁₀₀

⇒ 241.5 = ^{115 m}/₁₀₀

After cross multiplication, we get

241.5 × 100 = 115 m

⇒ 115 m = 241.5 × 100

⇒ m = ^{241.5 × 100}/₁₁₅

⇒ m = ²⁴¹⁵⁰/₁₁₅ = 210

⇒ m = 210

Thus, the Cost Price (CP) = $210 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) = $241.5

And, the profit = 15%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 15% of 100 = 15

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

⇒ Sale Price (SP) = 100 + 15

⇒ Sale Price (SP) = 115

∵ If the Sale Price (SP) is 115, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₁₁₅

∴ If the Sale Price (SP) is 241.5, then the Cost Price (CP)

= ¹⁰⁰/₁₁₅ × 241.5

= ^{100 × 241.5}/₁₁₅

= ²⁴¹⁵⁰/₁₁₅ = 210

Thus, the Cost Price (CP) = $210 Answer

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

Given, the sale price (SP) = $241.5

And, the profit = 15%

Then, the Cost Price (CP) = ?

SP = 115% of CP

⇒ SP = ¹¹⁵/₁₀₀ × CP

⇒ 241.5 = ^{115 CP}/₁₀₀

After cross multiplication

⇒ 241.5 × 100 = 115 CP

⇒ 115 CP = 241.5 × 100

⇒ CP = ^{241.5 × 100}/₁₁₅

⇒ CP = ²⁴¹⁵⁰/₁₁₅ = 210

⇒ CP = $210 Answer

Similar Questions

(1) Mr. Peter earns a profit of 110% by selling goods for $4431.00. For how much was he purchased those goods?

(2) Mr. Noah loses 37% by selling an article for $1077.30. For how much should he sell it to get a profit of 36%?

(3) Bill sold a bicycle for $640. If he purchased it at $800, then calculate his loss and loss percent in this sale.

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

(5) Find the cost price, if a trader gets a loss of 39% by selling 100 packets of fruits for $4642.10

(6) Mr. Peter buys 48 articles for $1 and sells 47 articles for $1. Find the profit percent.

(7) What will be the cost price, if a trader gets a loss of 2% by selling an article for $205.80?

(8) A peddler purchased 25 apples per $1 and sold them at a rate of 24 apples per $1. What will be the profit percent?

(9) A dealer loses 56% by selling an article for $1170.40. For how much should he sell it to get a profit of 55%?

(10) Find the cost price, if a trader earns a profit of 265% by selling an article for $19016.5