Profit And Loss
Math MCQs

Question :    After selling some items for $6884.50 Mr. Bob earns 145%. Find the cost price of those items.

Correct Answer  2810

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) = $6884.5

And, the profit = 145%

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 + 145} × 6884.5

= ^{100 × 6884.5}/₂₄₅

= ⁶⁸⁸⁴⁵⁰/₂₄₅ = 2810

Thus, the Cost Price (CP) = $2810 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 = 145%

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

= 145% of m

= 145% × m

= ¹⁴⁵/₁₀₀ × m

⇒ Profit = ^{145 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 6884.5 = m + ^{145 m}/₁₀₀

⇒ 6884.5 = ^{100 m + 145 m}/₁₀₀

⇒ 6884.5 = ^{245 m}/₁₀₀

After cross multiplication, we get

6884.5 × 100 = 245 m

⇒ 245 m = 6884.5 × 100

⇒ m = ^{6884.5 × 100}/₂₄₅

⇒ m = ⁶⁸⁸⁴⁵⁰/₂₄₅ = 2810

⇒ m = 2810

Thus, the Cost Price (CP) = $2810 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) = $6884.5

And, the profit = 145%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 145% of 100 = 145

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

⇒ Sale Price (SP) = 100 + 145

⇒ Sale Price (SP) = 245

∵ If the Sale Price (SP) is 245, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₂₄₅

∴ If the Sale Price (SP) is 6884.5, then the Cost Price (CP)

= ¹⁰⁰/₂₄₅ × 6884.5

= ^{100 × 6884.5}/₂₄₅

= ⁶⁸⁸⁴⁵⁰/₂₄₅ = 2810

Thus, the Cost Price (CP) = $2810 Answer

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

Given, the sale price (SP) = $6884.5

And, the profit = 145%

Then, the Cost Price (CP) = ?

SP = 245% of CP

⇒ SP = ²⁴⁵/₁₀₀ × CP

⇒ 6884.5 = ^{245 CP}/₁₀₀

After cross multiplication

⇒ 6884.5 × 100 = 245 CP

⇒ 245 CP = 6884.5 × 100

⇒ CP = ^{6884.5 × 100}/₂₄₅

⇒ CP = ⁶⁸⁸⁴⁵⁰/₂₄₅ = 2810

⇒ CP = $2810 Answer

Similar Questions

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(2) A trader loses 48% by selling an article for $1175.20. For how much should he sell it to get a profit of 47%?

(3) If a hawker bought 23 apples per $1 and sold them at a rate of 22 apples per $1, then what would his profit percent be?

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

(5) Calculate the earnings in percent if a vendor buys 72 coins for $1 and sells 71 coins for $1.

(6) Find the cost price, if Mrs. Julie earns a profit of 360% by selling some articles for $32706

(7) Mr. William buys 15 toffees for $1 and sells 14 tofees for $1. What is the profit percent?

(8) William loses 74% by selling an article for $925.60. For how much should he sell it to get a profit of 73%?

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

(10) Mr. Bob buys 40 articles for $1 and sells 39 articles for $1. Find the profit percent in this sale.