Profit And Loss
Math MCQs

Question :    By selling some goods for $3249 a shopkeeper earns a profit of 90%. Find the cost price of those goods.

Correct Answer  1710

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) = $3249

And, the profit = 90%

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 + 90} × 3249

= ^{100 × 3249}/₁₉₀

= ³²⁴⁹⁰⁰/₁₉₀ = 1710

Thus, the Cost Price (CP) = $1710 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 = 90%

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

= 90% of m

= 90% × m

= ⁹⁰/₁₀₀ × m

⇒ Profit = ^{90 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 3249 = m + ^{90 m}/₁₀₀

⇒ 3249 = ^{100 m + 90 m}/₁₀₀

⇒ 3249 = ^{190 m}/₁₀₀

After cross multiplication, we get

3249 × 100 = 190 m

⇒ 190 m = 3249 × 100

⇒ m = ^{3249 × 100}/₁₉₀

⇒ m = ³²⁴⁹⁰⁰/₁₉₀ = 1710

⇒ m = 1710

Thus, the Cost Price (CP) = $1710 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) = $3249

And, the profit = 90%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 90% of 100 = 90

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

⇒ Sale Price (SP) = 100 + 90

⇒ Sale Price (SP) = 190

∵ If the Sale Price (SP) is 190, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₁₉₀

∴ If the Sale Price (SP) is 3249, then the Cost Price (CP)

= ¹⁰⁰/₁₉₀ × 3249

= ^{100 × 3249}/₁₉₀

= ³²⁴⁹⁰⁰/₁₉₀ = 1710

Thus, the Cost Price (CP) = $1710 Answer

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

Given, the sale price (SP) = $3249

And, the profit = 90%

Then, the Cost Price (CP) = ?

SP = 190% of CP

⇒ SP = ¹⁹⁰/₁₀₀ × CP

⇒ 3249 = ^{190 CP}/₁₀₀

After cross multiplication

⇒ 3249 × 100 = 190 CP

⇒ 190 CP = 3249 × 100

⇒ CP = ^{3249 × 100}/₁₉₀

⇒ CP = ³²⁴⁹⁰⁰/₁₉₀ = 1710

⇒ CP = $1710 Answer

Similar Questions

(1) Mr. John buys 28 articles for $1 and sells 27 articles for $1 then, find his profit percent.

(2) A dealer sold an antique piece of a car $25771.50. If he earns a profit of 315%, then find his cost price.

(3) After selling some items for $6884.50 Mr. Bob earns 145%. Find the cost price of those items.

(4) John purchased a bicycle in an auction at $80 and sold it at $104. Calculate the profit and profit percent in this sale.

(5) A trader loses 52% by selling an article for $1180.80. For how much should he sell it to get a profit of 51%?

(6) William loses 71% by selling an article for $988.90. For how much should he sell it to get a profit of 70%?

(7) Mr. Steven loses 95% by selling an article for $230.50. For how much should he sell it to get a profit of 94%?

(8) Mr. Jack buys 13 articles for $1 and sells 12 articles for $1. Find his profit percent.

(9) Find the cost price, if a trader gets a loss of 47% by selling 500 kg rice for $4881.30

(10) Calculate the earnings percentage if a vendor buys 57 articles for $1 and sells 56 articles for $1.