Profit And Loss
Math MCQs

Question :    By selling a car for $4751.5 Mr. Aron earns a profit of 115%. For how much was he purchased his car?

Correct Answer  2210

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) = $4751.5

And, the profit = 115%

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 + 115} × 4751.5

= ^{100 × 4751.5}/₂₁₅

= ⁴⁷⁵¹⁵⁰/₂₁₅ = 2210

Thus, the Cost Price (CP) = $2210 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 = 115%

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

= 115% of m

= 115% × m

= ¹¹⁵/₁₀₀ × m

⇒ Profit = ^{115 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 4751.5 = m + ^{115 m}/₁₀₀

⇒ 4751.5 = ^{100 m + 115 m}/₁₀₀

⇒ 4751.5 = ^{215 m}/₁₀₀

After cross multiplication, we get

4751.5 × 100 = 215 m

⇒ 215 m = 4751.5 × 100

⇒ m = ^{4751.5 × 100}/₂₁₅

⇒ m = ⁴⁷⁵¹⁵⁰/₂₁₅ = 2210

⇒ m = 2210

Thus, the Cost Price (CP) = $2210 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) = $4751.5

And, the profit = 115%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 115% of 100 = 115

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

⇒ Sale Price (SP) = 100 + 115

⇒ Sale Price (SP) = 215

∵ If the Sale Price (SP) is 215, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₂₁₅

∴ If the Sale Price (SP) is 4751.5, then the Cost Price (CP)

= ¹⁰⁰/₂₁₅ × 4751.5

= ^{100 × 4751.5}/₂₁₅

= ⁴⁷⁵¹⁵⁰/₂₁₅ = 2210

Thus, the Cost Price (CP) = $2210 Answer

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

Given, the sale price (SP) = $4751.5

And, the profit = 115%

Then, the Cost Price (CP) = ?

SP = 215% of CP

⇒ SP = ²¹⁵/₁₀₀ × CP

⇒ 4751.5 = ^{215 CP}/₁₀₀

After cross multiplication

⇒ 4751.5 × 100 = 215 CP

⇒ 215 CP = 4751.5 × 100

⇒ CP = ^{4751.5 × 100}/₂₁₅

⇒ CP = ⁴⁷⁵¹⁵⁰/₂₁₅ = 2210

⇒ CP = $2210 Answer

Similar Questions

(1) Find the cost price, if a trader gets a loss of 40% by selling 1000 packets of fruits for $4686

(2) Find the cost price, if a trader gets a loss of 47% by selling 500 kg rice for $4881.30

(3) Mrs. Julie purchased 27 oranges for $1 and sold 26 oranges for $1. What will be his profit percentage?

(4) Mr. Donald loses 84% by selling an article for $649.60. For how much should he sell it to get a profit of 83%?

(5) A hawker buys 10 articles for $1 and sells 9 articles for $1 then, find the profit percent.

(6) Find the cost price, if a trader gets a loss of 38% by selling 600 packets of fruits for $4594.20

(7) Mr. Bob buys 40 articles for $1 and sells 39 articles for $1. Find the profit percent in this sale.

(8) Find the cost price, if a trader gets a loss of 63% by selling 15 TV sets for $4591.7

(9) If a vendor buys 14 chocolates for $1 and sells 13 chocolates for $1 then, what is his profit percent?

(10) Find the cost price, if a share broker gets a loss of 28% by selling 300 shares for $3895.20.