Profit And Loss
Math MCQs

Question :    How much Mr. Gates had to pay to purchase his motorbike? If he gets a profit of 70% after selling it for $2227.

Correct Answer  1310

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) = $2227

And, the profit = 70%

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 + 70} × 2227

= ^{100 × 2227}/₁₇₀

= ²²²⁷⁰⁰/₁₇₀ = 1310

Thus, the Cost Price (CP) = $1310 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 = 70%

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

= 70% of m

= 70% × m

= ⁷⁰/₁₀₀ × m

⇒ Profit = ^{70 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 2227 = m + ^{70 m}/₁₀₀

⇒ 2227 = ^{100 m + 70 m}/₁₀₀

⇒ 2227 = ^{170 m}/₁₀₀

After cross multiplication, we get

2227 × 100 = 170 m

⇒ 170 m = 2227 × 100

⇒ m = ^{2227 × 100}/₁₇₀

⇒ m = ²²²⁷⁰⁰/₁₇₀ = 1310

⇒ m = 1310

Thus, the Cost Price (CP) = $1310 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) = $2227

And, the profit = 70%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 70% of 100 = 70

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

⇒ Sale Price (SP) = 100 + 70

⇒ Sale Price (SP) = 170

∵ If the Sale Price (SP) is 170, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₁₇₀

∴ If the Sale Price (SP) is 2227, then the Cost Price (CP)

= ¹⁰⁰/₁₇₀ × 2227

= ^{100 × 2227}/₁₇₀

= ²²²⁷⁰⁰/₁₇₀ = 1310

Thus, the Cost Price (CP) = $1310 Answer

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

Given, the sale price (SP) = $2227

And, the profit = 70%

Then, the Cost Price (CP) = ?

SP = 170% of CP

⇒ SP = ¹⁷⁰/₁₀₀ × CP

⇒ 2227 = ^{170 CP}/₁₀₀

After cross multiplication

⇒ 2227 × 100 = 170 CP

⇒ 170 CP = 2227 × 100

⇒ CP = ^{2227 × 100}/₁₇₀

⇒ CP = ²²²⁷⁰⁰/₁₇₀ = 1310

⇒ CP = $1310 Answer

Similar Questions

(1) If a vendor buys 60 articles for $1 and sells 59 articles for $1 then, calculate the profit in percent.

(2) How much percent will John get if he buys 39 articles for $1 and sells at a rate of 38 articles per $1?

(3) If a broker loses 39% by selling some of his stocks for $1104.10 then he should sell them for how much to get a profit of 38%?

(4) Find the cost price, if a trader gets a loss of 61% by selling 4 TV sets for $4683.90

(5) Find the cost price, if a trader gets a loss of 19% by selling an article for $2924.10

(6) If a peddler bought 71 paper clips for $1 and sold 70 paper clips for $1 then, find the profit in percent.

(7) John sold rice at $7.20 per kg. If he purchased 120 kg of rice for $960, then calculate the loss and loss percent in this sale.

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

(9) Calculate the earnings in percent if a hawker buys 44 articles for $1 and sells 43 articles for $1.

(10) William loses 75% by selling an article for $902.50. For how much should he sell it to get a profit of 74%?