Profit And Loss
Math MCQs

Question :    A trader earns a profit of 170% by selling an article for $8937. Find the cost price.

Correct Answer  3310

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) = $8937

And, the profit = 170%

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 + 170} × 8937

= ^{100 × 8937}/₂₇₀

= ⁸⁹³⁷⁰⁰/₂₇₀ = 3310

Thus, the Cost Price (CP) = $3310 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 = 170%

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

= 170% of m

= 170% × m

= ¹⁷⁰/₁₀₀ × m

⇒ Profit = ^{170 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 8937 = m + ^{170 m}/₁₀₀

⇒ 8937 = ^{100 m + 170 m}/₁₀₀

⇒ 8937 = ^{270 m}/₁₀₀

After cross multiplication, we get

8937 × 100 = 270 m

⇒ 270 m = 8937 × 100

⇒ m = ^{8937 × 100}/₂₇₀

⇒ m = ⁸⁹³⁷⁰⁰/₂₇₀ = 3310

⇒ m = 3310

Thus, the Cost Price (CP) = $3310 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) = $8937

And, the profit = 170%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 170% of 100 = 170

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

⇒ Sale Price (SP) = 100 + 170

⇒ Sale Price (SP) = 270

∵ If the Sale Price (SP) is 270, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₂₇₀

∴ If the Sale Price (SP) is 8937, then the Cost Price (CP)

= ¹⁰⁰/₂₇₀ × 8937

= ^{100 × 8937}/₂₇₀

= ⁸⁹³⁷⁰⁰/₂₇₀ = 3310

Thus, the Cost Price (CP) = $3310 Answer

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

Given, the sale price (SP) = $8937

And, the profit = 170%

Then, the Cost Price (CP) = ?

SP = 270% of CP

⇒ SP = ²⁷⁰/₁₀₀ × CP

⇒ 8937 = ^{270 CP}/₁₀₀

After cross multiplication

⇒ 8937 × 100 = 270 CP

⇒ 270 CP = 8937 × 100

⇒ CP = ^{8937 × 100}/₂₇₀

⇒ CP = ⁸⁹³⁷⁰⁰/₂₇₀ = 3310

⇒ CP = $3310 Answer

Similar Questions

(1) By selling a house for $14332.50, a dealer earns a profit of 225%. Find the cost price

(2) Mrs. Julie purchased 27 oranges for $1 and sold 26 oranges for $1. What will be his profit percentage?

(3) Bill sold his secondhand motorcycle for $512.50. In this sale, he got a profit of 25%. For how much amount had he purchased the motorcycle?

(4) If a trader earned a profit of 350% by selling a housing plot for $31095 then, what was the cost price of the plot?

(5) Find the cost price, if a dealer earns a profit of 245% by selling a plot for $16594.5

(6) Find the cost price, if a trader gets a loss of 63% by selling 15 TV sets for $4591.7

(7) After selling some articles for $22269.00 a trader earns a profit of 290%. Find the cost price.

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

(9) William loses 43% by selling an article for $1145.70. For how much should he sell it to get a profit of 42%?

(10) If a trader gets a loss of 14% by selling some articles for $2244.60 then what was his cost price?