Profit And Loss
Math MCQs

Question :    Bill sold his secondhand motorcycle for $512.50. In this sale, he got a profit of 25%. For how much amount had he purchased the motorcycle?

Correct Answer  410

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) = $512.5

And, the profit = 25%

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 + 25} × 512.5

= ^{100 × 512.5}/₁₂₅

= ⁵¹²⁵⁰/₁₂₅ = 410

Thus, the Cost Price (CP) = $410 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 = 25%

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

= 25% of m

= 25% × m

= ²⁵/₁₀₀ × m

⇒ Profit = ^{25 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 512.5 = m + ^{25 m}/₁₀₀

⇒ 512.5 = ^{100 m + 25 m}/₁₀₀

⇒ 512.5 = ^{125 m}/₁₀₀

After cross multiplication, we get

512.5 × 100 = 125 m

⇒ 125 m = 512.5 × 100

⇒ m = ^{512.5 × 100}/₁₂₅

⇒ m = ⁵¹²⁵⁰/₁₂₅ = 410

⇒ m = 410

Thus, the Cost Price (CP) = $410 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) = $512.5

And, the profit = 25%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 25% of 100 = 25

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

⇒ Sale Price (SP) = 100 + 25

⇒ Sale Price (SP) = 125

∵ If the Sale Price (SP) is 125, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₁₂₅

∴ If the Sale Price (SP) is 512.5, then the Cost Price (CP)

= ¹⁰⁰/₁₂₅ × 512.5

= ^{100 × 512.5}/₁₂₅

= ⁵¹²⁵⁰/₁₂₅ = 410

Thus, the Cost Price (CP) = $410 Answer

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

Given, the sale price (SP) = $512.5

And, the profit = 25%

Then, the Cost Price (CP) = ?

SP = 125% of CP

⇒ SP = ¹²⁵/₁₀₀ × CP

⇒ 512.5 = ^{125 CP}/₁₀₀

After cross multiplication

⇒ 512.5 × 100 = 125 CP

⇒ 125 CP = 512.5 × 100

⇒ CP = ^{512.5 × 100}/₁₂₅

⇒ CP = ⁵¹²⁵⁰/₁₂₅ = 410

⇒ CP = $410 Answer

Similar Questions

(1) Find the cost price, if Mr. Oliver earns a profit of 150% by selling an article for $7275.00

(2) What was the cost price, if a trader gets a loss of 18% by selling some articles for $2796.20?

(3) If a book seller gets a loss of 33% by selling 300 books for $4294.70 then find the cost price of the books.

(4) John loses 62% by selling an article for $1124.80. For how much should he sell it to get a profit of 61%?

(5) While shifting to the other city, Mr. Bob sold all of the furniture and got a profit of 35%. If he sold them for $823.50, then for how much had he purchased them?

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

(7) William loses 75% by selling an article for $902.50. For how much should he sell it to get a profit of 74%?

(8) A dealer loses 23% by selling an article for $777.7. For how much should he sell it to get a profit of 22%?

(9) Mr. Robert sold his motorcycle for $1629 and got a loss of 10%. What was his cost price?

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