Profit And Loss
Math MCQs

Question :    Find the cost price, if a dealer earns a profit of 380% by selling an article for $36048

Correct Answer  7510

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) = $36048

And, the profit = 380%

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 + 380} × 36048

= ^{100 × 36048}/₄₈₀

= ^3604800/₄₈₀ = 7510

Thus, the Cost Price (CP) = $7510 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 = 380%

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

= 380% of m

= 380% × m

= ³⁸⁰/₁₀₀ × m

⇒ Profit = ^{380 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 36048 = m + ^{380 m}/₁₀₀

⇒ 36048 = ^{100 m + 380 m}/₁₀₀

⇒ 36048 = ^{480 m}/₁₀₀

After cross multiplication, we get

36048 × 100 = 480 m

⇒ 480 m = 36048 × 100

⇒ m = ^{36048 × 100}/₄₈₀

⇒ m = ^3604800/₄₈₀ = 7510

⇒ m = 7510

Thus, the Cost Price (CP) = $7510 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) = $36048

And, the profit = 380%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 380% of 100 = 380

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

⇒ Sale Price (SP) = 100 + 380

⇒ Sale Price (SP) = 480

∵ If the Sale Price (SP) is 480, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₄₈₀

∴ If the Sale Price (SP) is 36048, then the Cost Price (CP)

= ¹⁰⁰/₄₈₀ × 36048

= ^{100 × 36048}/₄₈₀

= ^3604800/₄₈₀ = 7510

Thus, the Cost Price (CP) = $7510 Answer

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

Given, the sale price (SP) = $36048

And, the profit = 380%

Then, the Cost Price (CP) = ?

SP = 480% of CP

⇒ SP = ⁴⁸⁰/₁₀₀ × CP

⇒ 36048 = ^{480 CP}/₁₀₀

After cross multiplication

⇒ 36048 × 100 = 480 CP

⇒ 480 CP = 36048 × 100

⇒ CP = ^{36048 × 100}/₄₈₀

⇒ CP = ^3604800/₄₈₀ = 7510

⇒ CP = $7510 Answer

Similar Questions

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

(2) Mr. Peter loses 44% by selling an article for $1153.60. For how much should he sell it to get a profit of 43%?

(3) Find the cost price, if a trader gets a loss of 64% by selling five TV sets for $4539.6

(4) If a peddler buys 46 articles for $1 and sells 45 articles for $1 then, find the earnings in percentage.

(5) Find the cost price, if a share broker gets a loss of 29% by selling 500 stocks for $3983.10

(6) Mr. Bobby earns a profit of 120% by selling a TV set for $5082. What was the cost price of the TV set?

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

(8) Find the cost price, if a trader earns a profit of 265% by selling an article for $19016.5

(9) For how much should a trader sell an item to get a profit of 49% if he loses 50% by selling it for $1180.00?

(10) If a vendor gets a loss of 21% by selling some apples for $3167.90 then what was the cost price of those apples?