Profit And Loss
Math MCQs

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

Correct Answer  6610

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) = $28753.5

And, the profit = 335%

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 + 335} × 28753.5

= ^{100 × 28753.5}/₄₃₅

= ^2875350/₄₃₅ = 6610

Thus, the Cost Price (CP) = $6610 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 = 335%

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

= 335% of m

= 335% × m

= ³³⁵/₁₀₀ × m

⇒ Profit = ^{335 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 28753.5 = m + ^{335 m}/₁₀₀

⇒ 28753.5 = ^{100 m + 335 m}/₁₀₀

⇒ 28753.5 = ^{435 m}/₁₀₀

After cross multiplication, we get

28753.5 × 100 = 435 m

⇒ 435 m = 28753.5 × 100

⇒ m = ^{28753.5 × 100}/₄₃₅

⇒ m = ^2875350/₄₃₅ = 6610

⇒ m = 6610

Thus, the Cost Price (CP) = $6610 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) = $28753.5

And, the profit = 335%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 335% of 100 = 335

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

⇒ Sale Price (SP) = 100 + 335

⇒ Sale Price (SP) = 435

∵ If the Sale Price (SP) is 435, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₄₃₅

∴ If the Sale Price (SP) is 28753.5, then the Cost Price (CP)

= ¹⁰⁰/₄₃₅ × 28753.5

= ^{100 × 28753.5}/₄₃₅

= ^2875350/₄₃₅ = 6610

Thus, the Cost Price (CP) = $6610 Answer

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

Given, the sale price (SP) = $28753.5

And, the profit = 335%

Then, the Cost Price (CP) = ?

SP = 435% of CP

⇒ SP = ⁴³⁵/₁₀₀ × CP

⇒ 28753.5 = ^{435 CP}/₁₀₀

After cross multiplication

⇒ 28753.5 × 100 = 435 CP

⇒ 435 CP = 28753.5 × 100

⇒ CP = ^{28753.5 × 100}/₄₃₅

⇒ CP = ^2875350/₄₃₅ = 6610

⇒ CP = $6610 Answer

Similar Questions

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(2) If a trader gets a loss of 20% by selling some apples for $3048, then find the cost price of those apples.

(3) Find the cost price, if a vendor gets a loss of 15% by selling some articles for $2388.50.

(4) Find the cost price, if a trader gets a loss of 58% by selling two TV sets for $4792.20

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(6) A dealer loses 23% by selling an article for $777.7. For how much should he sell it to get a profit of 22%?

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

(8) Find the cost price, if a dealer gets a loss of 30% by selling 300 stocks for $4067

(9) If a vendor purchased 73 coins for $1 and sells 72 coins for $1 then, find profit in percent.

(10) Find the earnings percentage if a peddler buys 51 articles for $1 and sells 50 articles for $1.