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) James loses 68% by selling an article for $1043.20. For how much should he sell it to get a profit of 67%?

(2) What will be the earnings in percent if a vendor buys 45 articles for $1 and sells 44 articles for $1?

(3) How much percent will John get if he buys 38 articles for $1 and sells 37 articles for $1?

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

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

(6) For how much should Mr. Bose sell his furniture to get a profit of 28%, if he loses 29% by selling it for $930.10?

(7) If a trader gets a loss of 4% by selling an article for $585.60 then, find the cost price.

(8) Mr. John sold his scoory for $1465.10 and got a loss of 9%. What was the cost price of the scooty?

(9) Calculate the earnings in percent if a hawker buys 44 articles for $1 and sells 43 articles for $1.

(10) Oliver loses 35% by selling an article for $1046.50. For how much should he sell it to get a profit of 34%?