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) If Mr. Steve buys 41 articles for $1 and sells 40 articles for $1 then find the profit percent.

(3) Mr. Oliver loses 79% by selling an article for $800.10. For how much should he sell it to get a profit of 78%?

(4) Mr. Oliver loses 80% by selling an article for $772.00. For how much should he sell it to get a profit of 79%?

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(6) Find the cost price, if a vendor gets a loss of 34% by selling some articles for $4362.60

(7) Find the cost price, if a dealer earns a profit of 345% by selling some goods for $30304.5

(8) Find the cost price, if a trader gets a loss of 73% by selling 100 bags of apples for $3890.70 then find the cost price of the apples.

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

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