Profit And Loss
Math MCQs

Question :    Find the cost price, if a trader earns a profit of 5% by selling an article for $10.5

Correct Answer  10

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) = $10.5

And, the profit = 5%

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 + 5} × 10.5

= ^{100 × 10.5}/₁₀₅

= ¹⁰⁵⁰/₁₀₅ = 10

Thus, the Cost Price (CP) = $10 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 = 5%

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

= 5% of m

= 5% × m

= ⁵/₁₀₀ × m

⇒ Profit = ^{5 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 10.5 = m + ^{5 m}/₁₀₀

⇒ 10.5 = ^{100 m + 5 m}/₁₀₀

⇒ 10.5 = ^{105 m}/₁₀₀

After cross multiplication, we get

10.5 × 100 = 105 m

⇒ 105 m = 10.5 × 100

⇒ m = ^{10.5 × 100}/₁₀₅

⇒ m = ¹⁰⁵⁰/₁₀₅ = 10

⇒ m = 10

Thus, the Cost Price (CP) = $10 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) = $10.5

And, the profit = 5%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 5% of 100 = 5

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

⇒ Sale Price (SP) = 100 + 5

⇒ Sale Price (SP) = 105

∵ If the Sale Price (SP) is 105, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₁₀₅

∴ If the Sale Price (SP) is 10.5, then the Cost Price (CP)

= ¹⁰⁰/₁₀₅ × 10.5

= ^{100 × 10.5}/₁₀₅

= ¹⁰⁵⁰/₁₀₅ = 10

Thus, the Cost Price (CP) = $10 Answer

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

Given, the sale price (SP) = $10.5

And, the profit = 5%

Then, the Cost Price (CP) = ?

SP = 105% of CP

⇒ SP = ¹⁰⁵/₁₀₀ × CP

⇒ 10.5 = ^{105 CP}/₁₀₀

After cross multiplication

⇒ 10.5 × 100 = 105 CP

⇒ 105 CP = 10.5 × 100

⇒ CP = ^{10.5 × 100}/₁₀₅

⇒ CP = ¹⁰⁵⁰/₁₀₅ = 10

⇒ CP = $10 Answer

Similar Questions

(1) Find the cost price, if a trader earns a profit of 5% by selling an article for $10.5

(2) If a broker gets a loss of 22% by selling 100 shares for $3283.80, then find the cost price of those shares.

(3) If Boby buys 69 pencils for $1 and sells them at a rate of 68 per $1 then, find the earnings in percentage.

(4) A dealer loses 59% by selling an article for $1152.10. For how much should he sell it to get a profit of 58%?

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

(6) If Mr. Steve buys 41 articles for $1 and sells 40 articles for $1 then find the profit percent.

(7) How much percent will Peter earn if he buys 37 articles for $1 and sells 36 articles for $1?

(8) A shopkeeper loses 46% by selling an article for $1166.40. For how much should he sell it to get a profit of 45%?

(9) Potter loses 89% by selling an article for $474.10. For how much should he sell it to get a profit of 88%?

(10) James loses 67% by selling an article for $1059.30. For how much should he sell it to get a profit of 66%?