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

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(2) What will be the profit percentage if a hawker buys 64 articles for $1 and sells 63 articles for $1?

(3) John purchased a bike for $500 and he sold it at a gain of 12%. Find the sale price of the bike.

(4) After selling an article for $1565.5 the shopkeeper earns a profit of 55%. For how much had he purchase that article?

(5) In an exhibition, a trader earns a profit of 75%. His total sale was $2467.50. Find the cost price.

(6) Mrs. Mary loses 19% by selling an article for $656.10. For how much should she sell it to get a profit of 18%?

(7) By selling an article for $1125.30 a vendor gets a loss of 7%. Calculate the cost price.

(8) If a broker gets a loss of 22% by selling 100 shares for $3283.80, then find the cost price of those shares.

(9) A trader loses 47% by selling an article for $1171.30. For how much should he sell it to get a profit of 46%?

(10) A fruit seller gets a loss of 6% by selling an his old stock for $949.40. What was his cost price?