Profit And Loss
Math MCQs

Question :    Find the cost price, if a dealer earns a profit of 250% by selling a plot for $17185

Correct Answer  4910

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) = $17185

And, the profit = 250%

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 + 250} × 17185

= ^{100 × 17185}/₃₅₀

= ^1718500/₃₅₀ = 4910

Thus, the Cost Price (CP) = $4910 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 = 250%

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

= 250% of m

= 250% × m

= ²⁵⁰/₁₀₀ × m

⇒ Profit = ^{250 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 17185 = m + ^{250 m}/₁₀₀

⇒ 17185 = ^{100 m + 250 m}/₁₀₀

⇒ 17185 = ^{350 m}/₁₀₀

After cross multiplication, we get

17185 × 100 = 350 m

⇒ 350 m = 17185 × 100

⇒ m = ^{17185 × 100}/₃₅₀

⇒ m = ^1718500/₃₅₀ = 4910

⇒ m = 4910

Thus, the Cost Price (CP) = $4910 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) = $17185

And, the profit = 250%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 250% of 100 = 250

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

⇒ Sale Price (SP) = 100 + 250

⇒ Sale Price (SP) = 350

∵ If the Sale Price (SP) is 350, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₃₅₀

∴ If the Sale Price (SP) is 17185, then the Cost Price (CP)

= ¹⁰⁰/₃₅₀ × 17185

= ^{100 × 17185}/₃₅₀

= ^1718500/₃₅₀ = 4910

Thus, the Cost Price (CP) = $4910 Answer

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

Given, the sale price (SP) = $17185

And, the profit = 250%

Then, the Cost Price (CP) = ?

SP = 350% of CP

⇒ SP = ³⁵⁰/₁₀₀ × CP

⇒ 17185 = ^{350 CP}/₁₀₀

After cross multiplication

⇒ 17185 × 100 = 350 CP

⇒ 350 CP = 17185 × 100

⇒ CP = ^{17185 × 100}/₃₅₀

⇒ CP = ^1718500/₃₅₀ = 4910

⇒ CP = $4910 Answer

Similar Questions

(1) Find the cost price, if Mr. Jojo earns a profit of 355% by selling some articles for $31895.5

(2) Find the cost price, if a trader gets a loss of 48% by selling 500 kg of rice for $4893.20

(3) If a vendor buys 60 articles for $1 and sells 59 articles for $1 then, calculate the profit in percent.

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

(5) Find the cost price, if a trader gets a loss of 37% by selling 500 packets of fruits for $4542.30

(6) Calculate the profit in percent if Mr. John buys 67 articles for $1 and sells 66 articles for $1.

(7) Bill sold his bicycle at a profit of 15%. If he purchased that bicycle at $200 then find the sale price of the cycle.

(8) Mrs. Julie purchased 26 oranges for $1 and sold 25 oranges for $1. What will be his profit percentage??

(9) A peddler buys 11 oranges for $1 and sells 10 oranges for $1 then, find his profit percent.

(10) Mr. Boby loses 15% by selling an article for $518.50. For how much should he sell it to get a profit of 14%?