Profit And Loss
Math MCQs

Question :    In a deal, Mr. Kart earns a profit of 85%. He got a total of $2978.50 in the deal. What was the cost price of this deal?

Correct Answer  1610

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) = $2978.5

And, the profit = 85%

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 + 85} × 2978.5

= ^{100 × 2978.5}/₁₈₅

= ²⁹⁷⁸⁵⁰/₁₈₅ = 1610

Thus, the Cost Price (CP) = $1610 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 = 85%

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

= 85% of m

= 85% × m

= ⁸⁵/₁₀₀ × m

⇒ Profit = ^{85 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 2978.5 = m + ^{85 m}/₁₀₀

⇒ 2978.5 = ^{100 m + 85 m}/₁₀₀

⇒ 2978.5 = ^{185 m}/₁₀₀

After cross multiplication, we get

2978.5 × 100 = 185 m

⇒ 185 m = 2978.5 × 100

⇒ m = ^{2978.5 × 100}/₁₈₅

⇒ m = ²⁹⁷⁸⁵⁰/₁₈₅ = 1610

⇒ m = 1610

Thus, the Cost Price (CP) = $1610 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) = $2978.5

And, the profit = 85%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 85% of 100 = 85

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

⇒ Sale Price (SP) = 100 + 85

⇒ Sale Price (SP) = 185

∵ If the Sale Price (SP) is 185, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₁₈₅

∴ If the Sale Price (SP) is 2978.5, then the Cost Price (CP)

= ¹⁰⁰/₁₈₅ × 2978.5

= ^{100 × 2978.5}/₁₈₅

= ²⁹⁷⁸⁵⁰/₁₈₅ = 1610

Thus, the Cost Price (CP) = $1610 Answer

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

Given, the sale price (SP) = $2978.5

And, the profit = 85%

Then, the Cost Price (CP) = ?

SP = 185% of CP

⇒ SP = ¹⁸⁵/₁₀₀ × CP

⇒ 2978.5 = ^{185 CP}/₁₀₀

After cross multiplication

⇒ 2978.5 × 100 = 185 CP

⇒ 185 CP = 2978.5 × 100

⇒ CP = ^{2978.5 × 100}/₁₈₅

⇒ CP = ²⁹⁷⁸⁵⁰/₁₈₅ = 1610

⇒ CP = $1610 Answer

Similar Questions

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

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

(4) Find the cost price, if a trader gets a loss of 1% by selling an article for $9.9

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

(6) Mr. Razor loses 45% by selling an article for $1160.50. For how much should he sell it to get a profit of 44%?

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

(8) To get a profit of 15% Mr. John should sell his old bicycle for how much, if he loses 16% by selling it for $554.40?

(9) A trader loses 54% by selling an article for $1177.60. For how much should he sell it to get a profit of 53%?

(10) Find the cost price, if a trader gets a loss of 57% by selling a TV set for $4820.30