Profit And Loss
Math MCQs

Question :    While shifting to the other city, Mr. Bob sold all of the furniture and got a profit of 35%. If he sold them for $823.50, then for how much had he purchased them?

Correct Answer  610

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) = $823.5

And, the profit = 35%

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 + 35} × 823.5

= ^{100 × 823.5}/₁₃₅

= ⁸²³⁵⁰/₁₃₅ = 610

Thus, the Cost Price (CP) = $610 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 = 35%

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

= 35% of m

= 35% × m

= ³⁵/₁₀₀ × m

⇒ Profit = ^{35 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 823.5 = m + ^{35 m}/₁₀₀

⇒ 823.5 = ^{100 m + 35 m}/₁₀₀

⇒ 823.5 = ^{135 m}/₁₀₀

After cross multiplication, we get

823.5 × 100 = 135 m

⇒ 135 m = 823.5 × 100

⇒ m = ^{823.5 × 100}/₁₃₅

⇒ m = ⁸²³⁵⁰/₁₃₅ = 610

⇒ m = 610

Thus, the Cost Price (CP) = $610 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) = $823.5

And, the profit = 35%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 35% of 100 = 35

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

⇒ Sale Price (SP) = 100 + 35

⇒ Sale Price (SP) = 135

∵ If the Sale Price (SP) is 135, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₁₃₅

∴ If the Sale Price (SP) is 823.5, then the Cost Price (CP)

= ¹⁰⁰/₁₃₅ × 823.5

= ^{100 × 823.5}/₁₃₅

= ⁸²³⁵⁰/₁₃₅ = 610

Thus, the Cost Price (CP) = $610 Answer

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

Given, the sale price (SP) = $823.5

And, the profit = 35%

Then, the Cost Price (CP) = ?

SP = 135% of CP

⇒ SP = ¹³⁵/₁₀₀ × CP

⇒ 823.5 = ^{135 CP}/₁₀₀

After cross multiplication

⇒ 823.5 × 100 = 135 CP

⇒ 135 CP = 823.5 × 100

⇒ CP = ^{823.5 × 100}/₁₃₅

⇒ CP = ⁸²³⁵⁰/₁₃₅ = 610

⇒ CP = $610 Answer

Similar Questions

(1) If a trader gets a loss of 72% by selling 15 bags of apples for $3978.80 then find the cost price of the apples.

(2) What was the cost price, if a trader gets a loss of 17% by selling an article for $2664.30?

(3) For how much should a trader sell an item to get a profit of 49% if he loses 50% by selling it for $1180.00?

(4) Find the cost price, if Mr. Jojo earns a profit of 355% by selling some articles for $31895.5

(5) Jack sold a TV set at $1584. If he purchased it at $1800, then calculate his loss and loss percent in this sale.

(6) Mr. Peter buys 48 articles for $1 and sells 47 articles for $1. Find the profit percent.

(7) Noah loses 76% by selling an article for $878.40. For how much should he sell it to get a profit of 75%?

(8) if a vendor bought 74 nibs for $1 and sells them at a rate of 73 per $1 then calculate the profit in percent.

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

(10) A shopkeeper earns a profit of 175% by selling some antique articles for $9377.50. What was the cost price of those antique articles?