Profit And Loss
Math MCQs

Question :    For how much had Mr. Robert purchased his motorcycle if he earns a profit of 60% by selling it for $1776?

Correct Answer  1110

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) = $1776

And, the profit = 60%

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 + 60} × 1776

= ^{100 × 1776}/₁₆₀

= ¹⁷⁷⁶⁰⁰/₁₆₀ = 1110

Thus, the Cost Price (CP) = $1110 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 = 60%

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

= 60% of m

= 60% × m

= ⁶⁰/₁₀₀ × m

⇒ Profit = ^{60 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 1776 = m + ^{60 m}/₁₀₀

⇒ 1776 = ^{100 m + 60 m}/₁₀₀

⇒ 1776 = ^{160 m}/₁₀₀

After cross multiplication, we get

1776 × 100 = 160 m

⇒ 160 m = 1776 × 100

⇒ m = ^{1776 × 100}/₁₆₀

⇒ m = ¹⁷⁷⁶⁰⁰/₁₆₀ = 1110

⇒ m = 1110

Thus, the Cost Price (CP) = $1110 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) = $1776

And, the profit = 60%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 60% of 100 = 60

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

⇒ Sale Price (SP) = 100 + 60

⇒ Sale Price (SP) = 160

∵ If the Sale Price (SP) is 160, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₁₆₀

∴ If the Sale Price (SP) is 1776, then the Cost Price (CP)

= ¹⁰⁰/₁₆₀ × 1776

= ^{100 × 1776}/₁₆₀

= ¹⁷⁷⁶⁰⁰/₁₆₀ = 1110

Thus, the Cost Price (CP) = $1110 Answer

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

Given, the sale price (SP) = $1776

And, the profit = 60%

Then, the Cost Price (CP) = ?

SP = 160% of CP

⇒ SP = ¹⁶⁰/₁₀₀ × CP

⇒ 1776 = ^{160 CP}/₁₀₀

After cross multiplication

⇒ 1776 × 100 = 160 CP

⇒ 160 CP = 1776 × 100

⇒ CP = ^{1776 × 100}/₁₆₀

⇒ CP = ¹⁷⁷⁶⁰⁰/₁₆₀ = 1110

⇒ CP = $1110 Answer

Similar Questions

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(2) What was the cost price, if a trader gets a loss of 18% by selling some articles for $2796.20?

(3) A shopkeeper gets a loss of 10% by selling an article for $324. For how much should he sell it to get a profit of 9%?

(4) If a trader gets a loss of 4% by selling an article for $585.60 then, find the cost price.

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

(6) The cost price of an article is $12, and the sale price is $15. Find the profit and profit percent.

(7) A broker loses 41% by selling an article for $1126.90. For how much should he sell it to get a profit of 40%?

(8) Find the cost price, if a trader gets a loss of 35% by selling some articles for $4426.50

(9) A dealer loses 28% by selling some articles for $907.20. For how much should he sell them to get a profit of 27%?

(10) A trader loses 55% by selling an article for $1174.50. For how much should he sell it to get a profit of 54%?