Profit And Loss
Math MCQs

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

Correct Answer  1010

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) = $1565.5

And, the profit = 55%

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 + 55} × 1565.5

= ^{100 × 1565.5}/₁₅₅

= ¹⁵⁶⁵⁵⁰/₁₅₅ = 1010

Thus, the Cost Price (CP) = $1010 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 = 55%

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

= 55% of m

= 55% × m

= ⁵⁵/₁₀₀ × m

⇒ Profit = ^{55 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 1565.5 = m + ^{55 m}/₁₀₀

⇒ 1565.5 = ^{100 m + 55 m}/₁₀₀

⇒ 1565.5 = ^{155 m}/₁₀₀

After cross multiplication, we get

1565.5 × 100 = 155 m

⇒ 155 m = 1565.5 × 100

⇒ m = ^{1565.5 × 100}/₁₅₅

⇒ m = ¹⁵⁶⁵⁵⁰/₁₅₅ = 1010

⇒ m = 1010

Thus, the Cost Price (CP) = $1010 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) = $1565.5

And, the profit = 55%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 55% of 100 = 55

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

⇒ Sale Price (SP) = 100 + 55

⇒ Sale Price (SP) = 155

∵ If the Sale Price (SP) is 155, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₁₅₅

∴ If the Sale Price (SP) is 1565.5, then the Cost Price (CP)

= ¹⁰⁰/₁₅₅ × 1565.5

= ^{100 × 1565.5}/₁₅₅

= ¹⁵⁶⁵⁵⁰/₁₅₅ = 1010

Thus, the Cost Price (CP) = $1010 Answer

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

Given, the sale price (SP) = $1565.5

And, the profit = 55%

Then, the Cost Price (CP) = ?

SP = 155% of CP

⇒ SP = ¹⁵⁵/₁₀₀ × CP

⇒ 1565.5 = ^{155 CP}/₁₀₀

After cross multiplication

⇒ 1565.5 × 100 = 155 CP

⇒ 155 CP = 1565.5 × 100

⇒ CP = ^{1565.5 × 100}/₁₅₅

⇒ CP = ¹⁵⁶⁵⁵⁰/₁₅₅ = 1010

⇒ CP = $1010 Answer

Similar Questions

(1) If a trader gets a loss of 66% by selling ten TV sets for $4423.40 then find the cost price of all those TV sets

(2) James loses 68% by selling an article for $1043.20. For how much should he sell it to get a profit of 67%?

(3) A dealer sold a plot for $26502.00. In this deal, if the dealer earns a profit of 320%, then find the cost price.

(4) A trader loses 30% by selling an article for $952. For how much should he sell it to get a profit of 29%?

(5) A dealer loses 58% by selling an article for $1159.20. For how much should he sell it to get a profit of 57%?

(6) Mollie purchased 150 kg of wheat at $1350. Due to some unavoidable circumstances, he had to sell the wheat at $7.20 per kg. Calculate his total loss and loss percent in this sale.

(7) How much percent will a vendor earn if he buys 36 articles for $1 and sells them at a rate of 35 articles per $1?

(8) For how much should he sell the bicycle to get a profit of 19%, if a shopkeeper loses 20% by selling it for $688?

(9) Find the cost price, if a trader gets a loss of 48% by selling 500 kg of rice for $4893.20

(10) 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%?