Profit And Loss
Math MCQs

Question :    A dealer sold a plot for $26502.00. In this deal, if the dealer earns a profit of 320%, then find the cost price.

Correct Answer  6310

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) = $26502

And, the profit = 320%

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 + 320} × 26502

= ^{100 × 26502}/₄₂₀

= ^2650200/₄₂₀ = 6310

Thus, the Cost Price (CP) = $6310 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 = 320%

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

= 320% of m

= 320% × m

= ³²⁰/₁₀₀ × m

⇒ Profit = ^{320 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 26502 = m + ^{320 m}/₁₀₀

⇒ 26502 = ^{100 m + 320 m}/₁₀₀

⇒ 26502 = ^{420 m}/₁₀₀

After cross multiplication, we get

26502 × 100 = 420 m

⇒ 420 m = 26502 × 100

⇒ m = ^{26502 × 100}/₄₂₀

⇒ m = ^2650200/₄₂₀ = 6310

⇒ m = 6310

Thus, the Cost Price (CP) = $6310 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) = $26502

And, the profit = 320%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 320% of 100 = 320

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

⇒ Sale Price (SP) = 100 + 320

⇒ Sale Price (SP) = 420

∵ If the Sale Price (SP) is 420, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₄₂₀

∴ If the Sale Price (SP) is 26502, then the Cost Price (CP)

= ¹⁰⁰/₄₂₀ × 26502

= ^{100 × 26502}/₄₂₀

= ^2650200/₄₂₀ = 6310

Thus, the Cost Price (CP) = $6310 Answer

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

Given, the sale price (SP) = $26502

And, the profit = 320%

Then, the Cost Price (CP) = ?

SP = 420% of CP

⇒ SP = ⁴²⁰/₁₀₀ × CP

⇒ 26502 = ^{420 CP}/₁₀₀

After cross multiplication

⇒ 26502 × 100 = 420 CP

⇒ 420 CP = 26502 × 100

⇒ CP = ^{26502 × 100}/₄₂₀

⇒ CP = ^2650200/₄₂₀ = 6310

⇒ CP = $6310 Answer

Similar Questions

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(2) A trader earns a profit of 205% by selling some articles for $12230.50. What was the cost price?

(3) Find the cost price, if a dealer gets a loss of 31% by selling 400 stocks for $4146.90

(4) A shopkeeper gets a loss of 10% by selling an article for $324. For how much should he sell it to get a profit of 9%?

(5) Find the cost price, if a trader earns a profit of 390% by selling an article for $37779

(6) For how much should Mr. Bose sell his furniture to get a profit of 28%, if he loses 29% by selling it for $930.10?

(7) If a dealer loses 61% by selling an article for $1134.90. For how much should he sell it to get a profit of 60%?

(8) Mr. Oliver loses 82% by selling an article for $712.80. For how much should he sell it to get a profit of 81%?

(9) A fruit seller gets a loss of 6% by selling an his old stock for $949.40. What was his cost price?

(10) Mr. Bob buys 40 articles for $1 and sells 39 articles for $1. Find the profit percent in this sale.