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

(1) By selling some items for $12741.00 a trader earns a profit of 210%. Find the cost price.

(2) A dealer loses 60% by selling an article for $1144.00. For how much should he sell it to get a profit of 59%?

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

(4) If a trader gets a loss of 14% by selling some articles for $2244.60 then what was his cost price?

(5) Mr. Bob gets a loss of 11% after selling an article for $364.90. For how much would he sell it to get a profit of 10%?

(6) Find the cost price, if a trader gets a loss of 47% by selling 500 kg rice for $4881.30

(7) A dealer loses 57% by selling an article for $1165.30. For how much should he sell it to get a profit of 56%?

(8) John purchased a bike for $500 and he sold it at a gain of 12%. Find the sale price of the bike.

(9) Find the cost price, if a trader gets a loss of 37% by selling 500 packets of fruits for $4542.30

(10) A vendor buys 33 articles for $1 and sells 32 articles for $1. How much percent will he earn in this?