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

(1) Noah loses 78% by selling an article for $827.20. For how much should he sell it to get a profit of 77%?

(2) Mr. John earns a profit of 190% by selling a old car for $10759. For how much had he purchased that house?

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

(4) For how much should he sell the bicycle to get a profit of 19%, if a shopkeeper loses 20% by selling it for $688?

(5) Mrs. John earned a profit of 330% by selling her car. If she sold her car for $27993, then find the cost price of the car.

(6) If a dealer earns a profit of 260% by selling an article for $18396.00. Find the cost price.

(7) Mr. Robert buys 31 articles for $1 and sells 30 articles for $1. Find the profit in percent.

(8) Mr. Oliver loses 34% by selling an article for $1029.60. For how much should he sell it to get a profit of 33%?

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

(10) What is the cost price if Mrs. Norrah gets a profit of 165% by selling some items for $8506.5