Profit And Loss
Math MCQs

Question :    If a trader earns a profit of 45% by selling an article for $1174.5, then find the cost price.

Correct Answer  810

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) = $1174.5

And, the profit = 45%

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 + 45} × 1174.5

= ^{100 × 1174.5}/₁₄₅

= ¹¹⁷⁴⁵⁰/₁₄₅ = 810

Thus, the Cost Price (CP) = $810 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 = 45%

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

= 45% of m

= 45% × m

= ⁴⁵/₁₀₀ × m

⇒ Profit = ^{45 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 1174.5 = m + ^{45 m}/₁₀₀

⇒ 1174.5 = ^{100 m + 45 m}/₁₀₀

⇒ 1174.5 = ^{145 m}/₁₀₀

After cross multiplication, we get

1174.5 × 100 = 145 m

⇒ 145 m = 1174.5 × 100

⇒ m = ^{1174.5 × 100}/₁₄₅

⇒ m = ¹¹⁷⁴⁵⁰/₁₄₅ = 810

⇒ m = 810

Thus, the Cost Price (CP) = $810 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) = $1174.5

And, the profit = 45%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 45% of 100 = 45

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

⇒ Sale Price (SP) = 100 + 45

⇒ Sale Price (SP) = 145

∵ If the Sale Price (SP) is 145, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₁₄₅

∴ If the Sale Price (SP) is 1174.5, then the Cost Price (CP)

= ¹⁰⁰/₁₄₅ × 1174.5

= ^{100 × 1174.5}/₁₄₅

= ¹¹⁷⁴⁵⁰/₁₄₅ = 810

Thus, the Cost Price (CP) = $810 Answer

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

Given, the sale price (SP) = $1174.5

And, the profit = 45%

Then, the Cost Price (CP) = ?

SP = 145% of CP

⇒ SP = ¹⁴⁵/₁₀₀ × CP

⇒ 1174.5 = ^{145 CP}/₁₀₀

After cross multiplication

⇒ 1174.5 × 100 = 145 CP

⇒ 145 CP = 1174.5 × 100

⇒ CP = ^{1174.5 × 100}/₁₄₅

⇒ CP = ¹¹⁷⁴⁵⁰/₁₄₅ = 810

⇒ CP = $810 Answer

Similar Questions

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(2) A peddler buys 11 oranges for $1 and sells 10 oranges for $1 then, find his profit percent.

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

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

(5) Mr. Donald loses 87% by selling an article for $547.30. For how much should he sell it to get a profit of 86%?

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

(7) If a vendor bought 20 apples per $1 and sold them at a rate of 19 apples per $1, then what would his profit percent be?

(8) Find the cost price, if a trader gets a loss of 68% by selling five bags of rice for $4291.20

(9) Mrs. John earned a profit of 330% by selling her car. If she sold her car for $27993, then find the cost price of the car.

(10) Find the cost price, if a trader gets a loss of 19% by selling an article for $2924.10