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) Find the cost price, if a share broker gets a loss of 27% by selling 200 shares for $3803.30.

(2) Find the cost price, if a shopkeeper earns a profit of 240% by selling an article for $16014

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

(4) Find the cost price, if a dealer gets a loss of 31% by selling 400 stocks for $4146.90

(5) A trader loses 42% by selling an article for $1136.80. For how much should he sell it to get a profit of 41%?

(6) Mrs. Jolly loses 18% by selling an article for $623.20. For how much should she sell it to get a profit of 17%?

(7) After selling some articles for $22269.00 a trader earns a profit of 290%. Find the cost price.

(8) If a vendor bought 62 candies for $1 and sold 61 candies per $1 then find the profit percent.

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

(10) Find the earnings percentage if a hawker buys 50 articles for $1 and sells 49 articles for $1.