Profit And Loss
Math MCQs

Question :    Find the cost price, if a shopkeeper earns a profit of 300% by selling some articles for $23640

Correct Answer  5910

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) = $23640

And, the profit = 300%

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 + 300} × 23640

= ^{100 × 23640}/₄₀₀

= ^2364000/₄₀₀ = 5910

Thus, the Cost Price (CP) = $5910 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 = 300%

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

= 300% of m

= 300% × m

= ³⁰⁰/₁₀₀ × m

⇒ Profit = ^{300 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 23640 = m + ^{300 m}/₁₀₀

⇒ 23640 = ^{100 m + 300 m}/₁₀₀

⇒ 23640 = ^{400 m}/₁₀₀

After cross multiplication, we get

23640 × 100 = 400 m

⇒ 400 m = 23640 × 100

⇒ m = ^{23640 × 100}/₄₀₀

⇒ m = ^2364000/₄₀₀ = 5910

⇒ m = 5910

Thus, the Cost Price (CP) = $5910 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) = $23640

And, the profit = 300%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 300% of 100 = 300

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

⇒ Sale Price (SP) = 100 + 300

⇒ Sale Price (SP) = 400

∵ If the Sale Price (SP) is 400, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₄₀₀

∴ If the Sale Price (SP) is 23640, then the Cost Price (CP)

= ¹⁰⁰/₄₀₀ × 23640

= ^{100 × 23640}/₄₀₀

= ^2364000/₄₀₀ = 5910

Thus, the Cost Price (CP) = $5910 Answer

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

Given, the sale price (SP) = $23640

And, the profit = 300%

Then, the Cost Price (CP) = ?

SP = 400% of CP

⇒ SP = ⁴⁰⁰/₁₀₀ × CP

⇒ 23640 = ^{400 CP}/₁₀₀

After cross multiplication

⇒ 23640 × 100 = 400 CP

⇒ 400 CP = 23640 × 100

⇒ CP = ^{23640 × 100}/₄₀₀

⇒ CP = ^2364000/₄₀₀ = 5910

⇒ CP = $5910 Answer

Similar Questions

(1) Find the cost price, if a trader gets a loss of 67% by selling ten bags of apple for $4359.30

(2) Find the cost price if Mr. Rocky earns a profit of 105% by selling an article for $4120.50

(3) if a vendor bought 74 nibs for $1 and sells them at a rate of 73 per $1 then calculate the profit in percent.

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

(5) On a closing day, a shopkeeper earns a profit of 65%. If gets $1996.5 in total, then what was his cost price?

(6) Mr. Peter earns a profit of 110% by selling goods for $4431.00. For how much was he purchased those goods?

(7) Mr. Jojo buys 30 articles for $1 and sells 29 articles for $1. Find the profit in percent.

(8) Find the cost price, if a trader gets a loss of 63% by selling 15 TV sets for $4591.7

(9) If a shopkeeper earns a profit of 5% by selling an article at $210, then find the cost price of that article.

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