Profit And Loss
Math MCQs

Question :    A shopkeeper earns 130% after selling some old bikes for $5773. What was his cost price?

Correct Answer  2510

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) = $5773

And, the profit = 130%

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 + 130} × 5773

= ^{100 × 5773}/₂₃₀

= ⁵⁷⁷³⁰⁰/₂₃₀ = 2510

Thus, the Cost Price (CP) = $2510 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 = 130%

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

= 130% of m

= 130% × m

= ¹³⁰/₁₀₀ × m

⇒ Profit = ^{130 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 5773 = m + ^{130 m}/₁₀₀

⇒ 5773 = ^{100 m + 130 m}/₁₀₀

⇒ 5773 = ^{230 m}/₁₀₀

After cross multiplication, we get

5773 × 100 = 230 m

⇒ 230 m = 5773 × 100

⇒ m = ^{5773 × 100}/₂₃₀

⇒ m = ⁵⁷⁷³⁰⁰/₂₃₀ = 2510

⇒ m = 2510

Thus, the Cost Price (CP) = $2510 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) = $5773

And, the profit = 130%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 130% of 100 = 130

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

⇒ Sale Price (SP) = 100 + 130

⇒ Sale Price (SP) = 230

∵ If the Sale Price (SP) is 230, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₂₃₀

∴ If the Sale Price (SP) is 5773, then the Cost Price (CP)

= ¹⁰⁰/₂₃₀ × 5773

= ^{100 × 5773}/₂₃₀

= ⁵⁷⁷³⁰⁰/₂₃₀ = 2510

Thus, the Cost Price (CP) = $2510 Answer

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

Given, the sale price (SP) = $5773

And, the profit = 130%

Then, the Cost Price (CP) = ?

SP = 230% of CP

⇒ SP = ²³⁰/₁₀₀ × CP

⇒ 5773 = ^{230 CP}/₁₀₀

After cross multiplication

⇒ 5773 × 100 = 230 CP

⇒ 230 CP = 5773 × 100

⇒ CP = ^{5773 × 100}/₂₃₀

⇒ CP = ⁵⁷⁷³⁰⁰/₂₃₀ = 2510

⇒ CP = $2510 Answer

Similar Questions

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(2) Find the cost price, if a trader gets a loss of 64% by selling five TV sets for $4539.6

(3) After selling an article for $1565.5 the shopkeeper earns a profit of 55%. For how much had he purchase that article?

(4) Noah loses 77% by selling an article for $853.30. For how much should he sell it to get a profit of 76%?

(5) If a trader gets a loss of 24% by selling 500 shares for $3503.60 then find the cost price of those shares.

(6) A dealer loses 59% by selling an article for $1152.10. For how much should he sell it to get a profit of 58%?

(7) What will be the profit in percent if a vendor buys 70 paper clips for $1 and sells at a rate of 69 per $1?

(8) A hawker buys 19 articles for $1 and sold then at the rate of 18 articles per $1. What was this profit percent?

(9) Mr. James loses 24% after selling an article for $805.60. For how much should he sell it to get a profit of 23%?

(10) A broker loses 41% by selling an article for $1126.90. For how much should he sell it to get a profit of 40%?