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

(2) Find the cost price, if a trader earns a profit of 390% by selling an article for $37779

(3) If a trader gets a loss of 24% by selling 500 shares for $3503.60 then find the cost price of those shares.

(4) Find the cost price, if a share broker gets a loss of 27% by selling 200 shares for $3803.30.

(5) Find the cost price, if a share broker gets a loss of 29% by selling 500 stocks for $3983.10

(6) What will be thr profit in percent if a vendor purchased 76 pins for $1 and sold 75 pins for $1?

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

(8) A dealer earns a profit of 285% by selling some items for $21598.50. What was his cost price?

(9) By selling an article for $15443.50, Mrs. Linda earns a profit of 235%. What was the cost price?

(10) John purchased a bicycle in an auction at $80 and sold it at $104. Calculate the profit and profit percent in this sale.