Profit And Loss
Math MCQs

Question :    A shopkeeper earns a profit of 125% after selling some items for $5422.50. Find the cost price of those items.

Correct Answer  2410

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) = $5422.5

And, the profit = 125%

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 + 125} × 5422.5

= ^{100 × 5422.5}/₂₂₅

= ⁵⁴²²⁵⁰/₂₂₅ = 2410

Thus, the Cost Price (CP) = $2410 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 = 125%

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

= 125% of m

= 125% × m

= ¹²⁵/₁₀₀ × m

⇒ Profit = ^{125 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 5422.5 = m + ^{125 m}/₁₀₀

⇒ 5422.5 = ^{100 m + 125 m}/₁₀₀

⇒ 5422.5 = ^{225 m}/₁₀₀

After cross multiplication, we get

5422.5 × 100 = 225 m

⇒ 225 m = 5422.5 × 100

⇒ m = ^{5422.5 × 100}/₂₂₅

⇒ m = ⁵⁴²²⁵⁰/₂₂₅ = 2410

⇒ m = 2410

Thus, the Cost Price (CP) = $2410 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) = $5422.5

And, the profit = 125%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 125% of 100 = 125

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

⇒ Sale Price (SP) = 100 + 125

⇒ Sale Price (SP) = 225

∵ If the Sale Price (SP) is 225, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₂₂₅

∴ If the Sale Price (SP) is 5422.5, then the Cost Price (CP)

= ¹⁰⁰/₂₂₅ × 5422.5

= ^{100 × 5422.5}/₂₂₅

= ⁵⁴²²⁵⁰/₂₂₅ = 2410

Thus, the Cost Price (CP) = $2410 Answer

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

Given, the sale price (SP) = $5422.5

And, the profit = 125%

Then, the Cost Price (CP) = ?

SP = 225% of CP

⇒ SP = ²²⁵/₁₀₀ × CP

⇒ 5422.5 = ^{225 CP}/₁₀₀

After cross multiplication

⇒ 5422.5 × 100 = 225 CP

⇒ 225 CP = 5422.5 × 100

⇒ CP = ^{5422.5 × 100}/₂₂₅

⇒ CP = ⁵⁴²²⁵⁰/₂₂₅ = 2410

⇒ CP = $2410 Answer

Similar Questions

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(2) Find the earnings percentage if a hawker buys 50 articles for $1 and sells 49 articles for $1.

(3) What was the cost price, if a trader earns a profit of 340% by selling a plot for $29524.00?

(4) A peddler purchased 25 apples per $1 and sold them at a rate of 24 apples per $1. What will be the profit percent?

(5) Mr. Boby loses 15% by selling an article for $518.50. For how much should he sell it to get a profit of 14%?

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

(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 share broker gets a loss of 29% by selling 500 stocks for $3983.10

(9) For how much should he sell it to get a profit of 16%, if Mr. Bond loses 17% by selling a bicycle for $589.30?

(10) Calculate the earnings percentage if a vendor buys 57 articles for $1 and sells 56 articles for $1.