Profit And Loss
Math MCQs

Question :    Find the cost price, if a shopkeeper earns a profit of 240% by selling an article for $16014

Correct Answer  4710

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) = $16014

And, the profit = 240%

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 + 240} × 16014

= ^{100 × 16014}/₃₄₀

= ^1601400/₃₄₀ = 4710

Thus, the Cost Price (CP) = $4710 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 = 240%

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

= 240% of m

= 240% × m

= ²⁴⁰/₁₀₀ × m

⇒ Profit = ^{240 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 16014 = m + ^{240 m}/₁₀₀

⇒ 16014 = ^{100 m + 240 m}/₁₀₀

⇒ 16014 = ^{340 m}/₁₀₀

After cross multiplication, we get

16014 × 100 = 340 m

⇒ 340 m = 16014 × 100

⇒ m = ^{16014 × 100}/₃₄₀

⇒ m = ^1601400/₃₄₀ = 4710

⇒ m = 4710

Thus, the Cost Price (CP) = $4710 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) = $16014

And, the profit = 240%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 240% of 100 = 240

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

⇒ Sale Price (SP) = 100 + 240

⇒ Sale Price (SP) = 340

∵ If the Sale Price (SP) is 340, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₃₄₀

∴ If the Sale Price (SP) is 16014, then the Cost Price (CP)

= ¹⁰⁰/₃₄₀ × 16014

= ^{100 × 16014}/₃₄₀

= ^1601400/₃₄₀ = 4710

Thus, the Cost Price (CP) = $4710 Answer

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

Given, the sale price (SP) = $16014

And, the profit = 240%

Then, the Cost Price (CP) = ?

SP = 340% of CP

⇒ SP = ³⁴⁰/₁₀₀ × CP

⇒ 16014 = ^{340 CP}/₁₀₀

After cross multiplication

⇒ 16014 × 100 = 340 CP

⇒ 340 CP = 16014 × 100

⇒ CP = ^{16014 × 100}/₃₄₀

⇒ CP = ^1601400/₃₄₀ = 4710

⇒ CP = $4710 Answer

Similar Questions

(1) Mrs. Mary earns a profit of 230% after selling an article for $14883. Find the cost price.

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

(3) A dealer gets a loss of 7% by selling an article for $195.30 then, for how much should he sell it to get a profit of 6%?

(4) Find the cost price, if Mrs. Julie earns a profit of 360% by selling some articles for $32706

(5) Find the cost price, if a trader gets a loss of 61% by selling 4 TV sets for $4683.90

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

(7) What will be thr profit in percent if a vendor purchased 76 pins for $1 and sold 75 pins for $1?

(8) Find the cost price, if a vendor gets a loss of 15% by selling some articles for $2388.50.

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

(10) A shopkeeper loses 31% by selling an article for $972.90. For how much should he sell it to get a profit of 30%?