Profit And Loss
Math MCQs

Question :    What is the cost price if a trader earns a profit of 155% by selling an article for $7675.50

Correct Answer  3010

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) = $7675.5

And, the profit = 155%

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 + 155} × 7675.5

= ^{100 × 7675.5}/₂₅₅

= ⁷⁶⁷⁵⁵⁰/₂₅₅ = 3010

Thus, the Cost Price (CP) = $3010 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 = 155%

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

= 155% of m

= 155% × m

= ¹⁵⁵/₁₀₀ × m

⇒ Profit = ^{155 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 7675.5 = m + ^{155 m}/₁₀₀

⇒ 7675.5 = ^{100 m + 155 m}/₁₀₀

⇒ 7675.5 = ^{255 m}/₁₀₀

After cross multiplication, we get

7675.5 × 100 = 255 m

⇒ 255 m = 7675.5 × 100

⇒ m = ^{7675.5 × 100}/₂₅₅

⇒ m = ⁷⁶⁷⁵⁵⁰/₂₅₅ = 3010

⇒ m = 3010

Thus, the Cost Price (CP) = $3010 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) = $7675.5

And, the profit = 155%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 155% of 100 = 155

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

⇒ Sale Price (SP) = 100 + 155

⇒ Sale Price (SP) = 255

∵ If the Sale Price (SP) is 255, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₂₅₅

∴ If the Sale Price (SP) is 7675.5, then the Cost Price (CP)

= ¹⁰⁰/₂₅₅ × 7675.5

= ^{100 × 7675.5}/₂₅₅

= ⁷⁶⁷⁵⁵⁰/₂₅₅ = 3010

Thus, the Cost Price (CP) = $3010 Answer

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

Given, the sale price (SP) = $7675.5

And, the profit = 155%

Then, the Cost Price (CP) = ?

SP = 255% of CP

⇒ SP = ²⁵⁵/₁₀₀ × CP

⇒ 7675.5 = ^{255 CP}/₁₀₀

After cross multiplication

⇒ 7675.5 × 100 = 255 CP

⇒ 255 CP = 7675.5 × 100

⇒ CP = ^{7675.5 × 100}/₂₅₅

⇒ CP = ⁷⁶⁷⁵⁵⁰/₂₅₅ = 3010

⇒ CP = $3010 Answer

Similar Questions

(1) Potter loses 90% by selling an article for $436. For how much should he sell it to get a profit of 89%?

(2) For how much should Mr. Bose sell his furniture to get a profit of 28%, if he loses 29% by selling it for $930.10?

(3) For how much should Mr. John sell it to get a profit of 3% if he loses 4% by selling an article for $57.60?

(4) Find the cost price, if Mrs. Barbara earns a profit of 275% by selling some items for $20287.50

(5) A dealer sold a plot for $26502.00. In this deal, if the dealer earns a profit of 320%, then find the cost price.

(6) Noah loses 76% by selling an article for $878.40. For how much should he sell it to get a profit of 75%?

(7) John loses 63% by selling an article for $1113.70. For how much should he sell it to get a profit of 62%?

(8) For how much should he sell it to get a profit of 16%, if Mr. Bond loses 17% by selling a bicycle for $589.30?

(9) If a seller bought 24 apples per $1 and sold them at a rate of 23 apples per $1, then what would his profit percent be?

(10) William loses 72% by selling an article for $968.80. For how much should he sell it to get a profit of 71%?