Profit And Loss
Math MCQs

Question :    A dealer earns a profit of 285% by selling some items for $21598.50. What was his cost price?

Correct Answer  5610

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) = $21598.5

And, the profit = 285%

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 + 285} × 21598.5

= ^{100 × 21598.5}/₃₈₅

= ^2159850/₃₈₅ = 5610

Thus, the Cost Price (CP) = $5610 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 = 285%

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

= 285% of m

= 285% × m

= ²⁸⁵/₁₀₀ × m

⇒ Profit = ^{285 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 21598.5 = m + ^{285 m}/₁₀₀

⇒ 21598.5 = ^{100 m + 285 m}/₁₀₀

⇒ 21598.5 = ^{385 m}/₁₀₀

After cross multiplication, we get

21598.5 × 100 = 385 m

⇒ 385 m = 21598.5 × 100

⇒ m = ^{21598.5 × 100}/₃₈₅

⇒ m = ^2159850/₃₈₅ = 5610

⇒ m = 5610

Thus, the Cost Price (CP) = $5610 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) = $21598.5

And, the profit = 285%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 285% of 100 = 285

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

⇒ Sale Price (SP) = 100 + 285

⇒ Sale Price (SP) = 385

∵ If the Sale Price (SP) is 385, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₃₈₅

∴ If the Sale Price (SP) is 21598.5, then the Cost Price (CP)

= ¹⁰⁰/₃₈₅ × 21598.5

= ^{100 × 21598.5}/₃₈₅

= ^2159850/₃₈₅ = 5610

Thus, the Cost Price (CP) = $5610 Answer

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

Given, the sale price (SP) = $21598.5

And, the profit = 285%

Then, the Cost Price (CP) = ?

SP = 385% of CP

⇒ SP = ³⁸⁵/₁₀₀ × CP

⇒ 21598.5 = ^{385 CP}/₁₀₀

After cross multiplication

⇒ 21598.5 × 100 = 385 CP

⇒ 385 CP = 21598.5 × 100

⇒ CP = ^{21598.5 × 100}/₃₈₅

⇒ CP = ^2159850/₃₈₅ = 5610

⇒ CP = $5610 Answer

Similar Questions

(1) Mr. Jack buys 13 articles for $1 and sells 12 articles for $1. Find his profit percent.

(2) Find the cost price, if a broker earns a profit of 385% by selling an article for $36908.5

(3) After selling some articles for $13261.50, a trader earns a profit of 215%. Find the cost price.

(4) Mr. Oliver loses 79% by selling an article for $800.10. For how much should he sell it to get a profit of 78%?

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

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

(7) Find the cost price, if a trader gets a loss of 51% by selling 200 bags of rice for $4904.90

(8) Mr. Donald loses 84% by selling an article for $649.60. For how much should he sell it to get a profit of 83%?

(9) Find the cost price, if a trader gets a loss of 49% by selling 1500 kg rice for $4901.10

(10) William loses 33% by selling an article for $1011.70. For how much should he sell it to get a profit of 32%?