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) If a hawker bought 63 candies for $1 and sold them at a rate of 62 candies per $1 then, find the profit percent.

(2) A vendor buys 33 articles for $1 and sells 32 articles for $1. How much percent will he earn in this?

(3) Find the cost price of the plot, if a dealer earns a profit of 185% by selling the plot for $10288.5

(4) If Mr. Steve buys 41 articles for $1 and sells 40 articles for $1 then find the profit percent.

(5) In an auction, Mr. Jojo got $27242.5 for his antique bike. If he got a profit of 325% in this deal, then what was his cost price.?

(6) Mr. Steven loses 93% by selling an article for $315.70. For how much should he sell it to get a profit of 92%?

(7) Mr. Noah loses 37% by selling an article for $1077.30. For how much should he sell it to get a profit of 36%?

(8) If after selling 5 bags of rice for $1297.20 a shopkeeper gets a loss of 8% then what was the cost price of the rice?

(9) Find the cost price, if Mr. Oliver earns a profit of 150% by selling an article for $7275.00

(10) To get a profit of 15% Mr. John should sell his old bicycle for how much, if he loses 16% by selling it for $554.40?