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

(1) If Mrs. Julie earned a profit of 335% by selling her car for $28753.50 then, what was the cost price of the car?

(2) If a trader gets a loss of 71% by selling 150 bags of corn flakes for $4062.90 then find the cost price of the corn flakes.

(3) If a trader earned a profit of 350% by selling a housing plot for $31095 then, what was the cost price of the plot?

(4) A car dealer earns 135% by selling an old antique car for $6133.50. For how much had he purchased that car?

(5) A dealer loses 58% by selling an article for $1159.20. For how much should he sell it to get a profit of 57%?

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

(7) A trader loses 49% by selling an article for $1178.10. For how much should he sell it to get a profit of 48%?

(8) A dealer loses 56% by selling an article for $1170.40. For how much should he sell it to get a profit of 55%?

(9) Mr. Steven loses 96% by selling an article for $186.40. For how much should he sell it to get a profit of 95%?

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