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) What will be the profit in percent if a vendor buys 70 paper clips for $1 and sells at a rate of 69 per $1?

(2) Mr. Jojo buys 30 articles for $1 and sells 29 articles for $1. Find the profit in percent.

(3) Mr. Oliver loses 83% by selling an article for $681.70. For how much should he sell it to get a profit of 82%?

(4) If a broker gets a loss of 23% by selling 200 shares he had for $3395.70 then find the cost price of those shares.

(5) Find the cost price, if a trader gets a loss of 45% by selling 800 bags of fruits for $4845.50

(6) A hawker buys 19 articles for $1 and sold then at the rate of 18 articles per $1. What was this profit percent?

(7) If a shopkeeper earns a profit of 5% by selling an article at $210, then find the cost price of that article.

(8) Mr. Donald loses 86% by selling an article for $582.40. For how much should he sell it to get a profit of 85%?

(9) A trader loses 55% by selling an article for $1174.50. For how much should he sell it to get a profit of 54%?

(10) A broker earns a profit of 310% by selling a house for $25051. Find the cost price.