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) 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?

(2) While shifting to the other city, Mr. Bob sold all of the furniture and got a profit of 35%. If he sold them for $823.50, then for how much had he purchased them?

(3) Find the cost price, if a dealer earns a profit of 250% by selling a plot for $17185

(4) A street seller buys 8 articles for $1 and sells 7 articles for $1. Find the profit percent in this sale.

(5) If a peddler bought 71 paper clips for $1 and sold 70 paper clips for $1 then, find the profit in percent.

(6) If a trader gets a loss of 25% by selling some shares for $3607.50, then find the cost price of those shares.

(7) Find the earnings percentage if a vendor buys 53 articles for $1 and sells 52 articles for $1.

(8) Mrs. Rosy loses 25% by selling her stock shares for $832.50. For how much should she sell them to get a profit of 24%?

(9) Mr. Oliver loses 83% by selling an article for $681.70. For how much should he sell it to get a profit of 82%?

(10) Calculate the earnings percentage if a hawker buys 58 articles for $1 and sells 57 articles for $1.