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) William loses 69% by selling an article for $1026.10. For how much should he sell it to get a profit of 68%?

(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) If Noah buys 32 articles for $1 and sells them at a rate of 31 articles per $1 then, find his profit percent.

(4) Mrs. Julie buys 16 oranges for $1 and sells 15 oranges for $1. What is her profit percent in this sale?

(5) Find the cost price, if a dealer earns a profit of 345% by selling some goods for $30304.5

(6) How much percent will Peter earn if he buys 37 articles for $1 and sells 36 articles for $1?

(7) If a dealer loses 61% by selling an article for $1134.90. For how much should he sell it to get a profit of 60%?

(8) Mr. Henry loses 26% by selling an article for $858.4. For how much should he sell it to get a profit of 25%?

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

(10) A seller gets a profit of 7% by selling a TV set for $4280. If he would have sold it for $4200, then find his profit percent.