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

(1) William loses 69% by selling an article for $1026.10. For how much should he sell it to get a profit of 68%?

(2) If Boby buys 69 pencils for $1 and sells them at a rate of 68 per $1 then, find the earnings in percentage.

(3) Jack sold a TV set at $1584. If he purchased it at $1800, then calculate his loss and loss percent in this sale.

(4) A car dealer earns 135% by selling an old antique car for $6133.50. For how much had he purchased that car?

(5) What will the earnings in percent if a vendor buys 42 apples for $1 and sells at a rate of 41 apples per $1?

(6) For how much Mr. Peter should sell his books to get a profit of 11%? If he loses 12% by selling them for $404.80.

(7) If a vendor bought 20 apples per $1 and sold them at a rate of 19 apples per $1, then what would his profit percent be?

(8) Find the cost price, if a trader gets a loss of 60% by selling five TV sets for $4724

(9) If a trader gets a loss of 55% by selling 15 bags of fruits for $4864.50 then find the cost price of fruits.

(10) If a vendor buys 7 lemons for $1 and sells 6 lemons for $1 then, what is the profit percent in this sale?