Profit And Loss
Math MCQs

Question :    If a trader earns a profit of 10% by selling rice for $121 per kg, then find the cost price of the rice

Correct Answer  110

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) = $121

And, the profit = 10%

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 + 10} × 121

= ^{100 × 121}/₁₁₀

= ¹²¹⁰⁰/₁₁₀ = 110

Thus, the Cost Price (CP) = $110 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 = 10%

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

= 10% of m

= 10% × m

= ¹⁰/₁₀₀ × m

⇒ Profit = ^{10 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 121 = m + ^{10 m}/₁₀₀

⇒ 121 = ^{100 m + 10 m}/₁₀₀

⇒ 121 = ^{110 m}/₁₀₀

After cross multiplication, we get

121 × 100 = 110 m

⇒ 110 m = 121 × 100

⇒ m = ^{121 × 100}/₁₁₀

⇒ m = ¹²¹⁰⁰/₁₁₀ = 110

⇒ m = 110

Thus, the Cost Price (CP) = $110 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) = $121

And, the profit = 10%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 10% of 100 = 10

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

⇒ Sale Price (SP) = 100 + 10

⇒ Sale Price (SP) = 110

∵ If the Sale Price (SP) is 110, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₁₁₀

∴ If the Sale Price (SP) is 121, then the Cost Price (CP)

= ¹⁰⁰/₁₁₀ × 121

= ^{100 × 121}/₁₁₀

= ¹²¹⁰⁰/₁₁₀ = 110

Thus, the Cost Price (CP) = $110 Answer

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

Given, the sale price (SP) = $121

And, the profit = 10%

Then, the Cost Price (CP) = ?

SP = 110% of CP

⇒ SP = ¹¹⁰/₁₀₀ × CP

⇒ 121 = ^{110 CP}/₁₀₀

After cross multiplication

⇒ 121 × 100 = 110 CP

⇒ 110 CP = 121 × 100

⇒ CP = ^{121 × 100}/₁₁₀

⇒ CP = ¹²¹⁰⁰/₁₁₀ = 110

⇒ CP = $110 Answer

Similar Questions

(1) A trader loses 48% by selling an article for $1175.20. For how much should he sell it to get a profit of 47%?

(2) A share broker earns a profit of 400% by selling his shares for $39550. For how much had he purchased those shares?

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

(4) William loses 70% by selling an article for $1008.00 For how much should he sell it to get a profit of 69%?

(5) 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%?

(6) Calculate the earnings percentage if a vendor buys 54 articles for $1 and sells 53 articles for $1.

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

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

(9) Find the cost price, if a dealer earns a profit of 380% by selling an article for $36048

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