Profit And Loss
Math MCQs

Question :    A trader earns a profit of 95% by selling an article for $3529.50. What was his cost price?

Correct Answer  1810

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) = $3529.5

And, the profit = 95%

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 + 95} × 3529.5

= ^{100 × 3529.5}/₁₉₅

= ³⁵²⁹⁵⁰/₁₉₅ = 1810

Thus, the Cost Price (CP) = $1810 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 = 95%

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

= 95% of m

= 95% × m

= ⁹⁵/₁₀₀ × m

⇒ Profit = ^{95 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 3529.5 = m + ^{95 m}/₁₀₀

⇒ 3529.5 = ^{100 m + 95 m}/₁₀₀

⇒ 3529.5 = ^{195 m}/₁₀₀

After cross multiplication, we get

3529.5 × 100 = 195 m

⇒ 195 m = 3529.5 × 100

⇒ m = ^{3529.5 × 100}/₁₉₅

⇒ m = ³⁵²⁹⁵⁰/₁₉₅ = 1810

⇒ m = 1810

Thus, the Cost Price (CP) = $1810 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) = $3529.5

And, the profit = 95%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 95% of 100 = 95

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

⇒ Sale Price (SP) = 100 + 95

⇒ Sale Price (SP) = 195

∵ If the Sale Price (SP) is 195, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₁₉₅

∴ If the Sale Price (SP) is 3529.5, then the Cost Price (CP)

= ¹⁰⁰/₁₉₅ × 3529.5

= ^{100 × 3529.5}/₁₉₅

= ³⁵²⁹⁵⁰/₁₉₅ = 1810

Thus, the Cost Price (CP) = $1810 Answer

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

Given, the sale price (SP) = $3529.5

And, the profit = 95%

Then, the Cost Price (CP) = ?

SP = 195% of CP

⇒ SP = ¹⁹⁵/₁₀₀ × CP

⇒ 3529.5 = ^{195 CP}/₁₀₀

After cross multiplication

⇒ 3529.5 × 100 = 195 CP

⇒ 195 CP = 3529.5 × 100

⇒ CP = ^{3529.5 × 100}/₁₉₅

⇒ CP = ³⁵²⁹⁵⁰/₁₉₅ = 1810

⇒ CP = $1810 Answer

Similar Questions

(1) Mr. Bob gets a loss of 11% after selling an article for $364.90. For how much would he sell it to get a profit of 10%?

(2) Find the cost price, if a shopkeeper earns a profit of 300% by selling some articles for $23640

(3) If a shopkeeper gets a loss of 65% by selling five TV sets for $4483.50 then find the cost price of all those TV sets.

(4) For how much had Mr. Robert purchased his motorcycle if he earns a profit of 60% by selling it for $1776?

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

(6) Find the cost price, if a trader gets a loss of 36% by selling 500 packets of fruits for $4486.40

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

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

(9) James loses 65% by selling an article for $1088.50. For how much should he sell it to get a profit of 64%?

(10) Bill sold a bicycle for $840. If he purchased it at $600, then calculate his profit and profit percent in this sale.