Profit And Loss
Math MCQs

Question :    Mr. Peter earns a profit of 110% by selling goods for $4431.00. For how much was he purchased those goods?

Correct Answer  2110

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) = $4431

And, the profit = 110%

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 + 110} × 4431

= ^{100 × 4431}/₂₁₀

= ⁴⁴³¹⁰⁰/₂₁₀ = 2110

Thus, the Cost Price (CP) = $2110 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 = 110%

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

= 110% of m

= 110% × m

= ¹¹⁰/₁₀₀ × m

⇒ Profit = ^{110 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 4431 = m + ^{110 m}/₁₀₀

⇒ 4431 = ^{100 m + 110 m}/₁₀₀

⇒ 4431 = ^{210 m}/₁₀₀

After cross multiplication, we get

4431 × 100 = 210 m

⇒ 210 m = 4431 × 100

⇒ m = ^{4431 × 100}/₂₁₀

⇒ m = ⁴⁴³¹⁰⁰/₂₁₀ = 2110

⇒ m = 2110

Thus, the Cost Price (CP) = $2110 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) = $4431

And, the profit = 110%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 110% of 100 = 110

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

⇒ Sale Price (SP) = 100 + 110

⇒ Sale Price (SP) = 210

∵ If the Sale Price (SP) is 210, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₂₁₀

∴ If the Sale Price (SP) is 4431, then the Cost Price (CP)

= ¹⁰⁰/₂₁₀ × 4431

= ^{100 × 4431}/₂₁₀

= ⁴⁴³¹⁰⁰/₂₁₀ = 2110

Thus, the Cost Price (CP) = $2110 Answer

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

Given, the sale price (SP) = $4431

And, the profit = 110%

Then, the Cost Price (CP) = ?

SP = 210% of CP

⇒ SP = ²¹⁰/₁₀₀ × CP

⇒ 4431 = ^{210 CP}/₁₀₀

After cross multiplication

⇒ 4431 × 100 = 210 CP

⇒ 210 CP = 4431 × 100

⇒ CP = ^{4431 × 100}/₂₁₀

⇒ CP = ⁴⁴³¹⁰⁰/₂₁₀ = 2110

⇒ CP = $2110 Answer

Similar Questions

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(2) Find the cost price, if Mr. Oliver earns a profit of 150% by selling an article for $7275.00

(3) Potter loses 91% by selling an article for $396.90. For how much should he sell it to get a profit of 90%?

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

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

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

(7) After selling some items for $6884.50 Mr. Bob earns 145%. Find the cost price of those items.

(8) A shopkeeper earns a profit of 125% after selling some items for $5422.50. Find the cost price of those items.

(9) After selling some antique items for $6504 a trader earns a profit of 140%. Find the cost price of those antique items.

(10) If Mr. Peter buys 17 apples for $1 and sells 16 apples for $1 then, find the profit percent in this sale.