Profit And Loss
Math MCQs

Question :    A share broker earns a profit of 400% by selling his shares for $39550. For how much had he purchased those shares?

Correct Answer  7910

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) = $39550

And, the profit = 400%

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 + 400} × 39550

= ^{100 × 39550}/₅₀₀

= ^3955000/₅₀₀ = 7910

Thus, the Cost Price (CP) = $7910 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 = 400%

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

= 400% of m

= 400% × m

= ⁴⁰⁰/₁₀₀ × m

⇒ Profit = ^{400 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 39550 = m + ^{400 m}/₁₀₀

⇒ 39550 = ^{100 m + 400 m}/₁₀₀

⇒ 39550 = ^{500 m}/₁₀₀

After cross multiplication, we get

39550 × 100 = 500 m

⇒ 500 m = 39550 × 100

⇒ m = ^{39550 × 100}/₅₀₀

⇒ m = ^3955000/₅₀₀ = 7910

⇒ m = 7910

Thus, the Cost Price (CP) = $7910 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) = $39550

And, the profit = 400%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 400% of 100 = 400

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

⇒ Sale Price (SP) = 100 + 400

⇒ Sale Price (SP) = 500

∵ If the Sale Price (SP) is 500, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₅₀₀

∴ If the Sale Price (SP) is 39550, then the Cost Price (CP)

= ¹⁰⁰/₅₀₀ × 39550

= ^{100 × 39550}/₅₀₀

= ^3955000/₅₀₀ = 7910

Thus, the Cost Price (CP) = $7910 Answer

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

Given, the sale price (SP) = $39550

And, the profit = 400%

Then, the Cost Price (CP) = ?

SP = 500% of CP

⇒ SP = ⁵⁰⁰/₁₀₀ × CP

⇒ 39550 = ^{500 CP}/₁₀₀

After cross multiplication

⇒ 39550 × 100 = 500 CP

⇒ 500 CP = 39550 × 100

⇒ CP = ^{39550 × 100}/₅₀₀

⇒ CP = ^3955000/₅₀₀ = 7910

⇒ CP = $7910 Answer

Similar Questions

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(2) Calculate the earnings percentage if a vendor buys 54 articles for $1 and sells 53 articles for $1.

(3) Mr. Oliver loses 82% by selling an article for $712.80. For how much should he sell it to get a profit of 81%?

(4) Mr. Steven loses 95% by selling an article for $230.50. For how much should he sell it to get a profit of 94%?

(5) Mrs. Mary loses 19% by selling an article for $656.10. For how much should she sell it to get a profit of 18%?

(6) What is the cost price; if a trader earns a profit of 295% by selling some articles for $22949.50?

(7) Oliver loses 35% by selling an article for $1046.50. For how much should he sell it to get a profit of 34%?

(8) Find the cost price, if a trader earns a profit of 390% by selling an article for $37779

(9) Find the cost price, if a trader gets a loss of 54% by selling 100 bags of mobile covers for $4880.60

(10) What is the cost price, if Mrs. Jill earns a profit of 200% by selling some items for $11730?