Profit And Loss
Math MCQs

Question :    For how much should he sell it to get a profit of 16%, if Mr. Bond loses 17% by selling a bicycle for $589.30?

Correct Answer  823.6

Solution & Explanation

Strategy to solve the question

Step (1) Calculate the cost price at given loss percent and the sale price.

Step (2) After gettting the cost price find the sale price at given profit percent.

Solution

Method (1) Formula Method

Finding the Sale Price to earn a profit using formula when the Sale Price at a loss is given

Given, the sale price (SP) = $589.3

And, the loss = 17%

Then, the Sale Price (SP) to earn a profit of 16% = ?

Formula to find the cost price when the sale price and loss percent are known

Cost Price (CP) = ¹⁰⁰/_{100 – gain%} × SP

Thus, the Cost Price (CP)

= ¹⁰⁰/_{100 – 17} × 589.3

= ¹⁰⁰/₈₃ × 589.3

= ^{100 × 589.3}/₈₃

= ⁵⁸⁹³⁰/₈₃ = 710

Thus, the Cost Price (CP) = $710

Finding the Sale Price using the formula when the cost price and Profit percent are known

Here now, CP = $710

And, profit = 16%

Thus Sale Price (SP) = ?

Formula to find the Sale Price (SP) when the cost price (CP) and profit percent are known

Sale Price (SP) = ^{100 + gain%}/₁₀₀ × Cost Price (CP)

Thus, the Sale Price (SP)

= ^{100 + 16}/₁₀₀ × 710

= ¹¹⁶/₁₀₀ × 710

= ^{116 × 710}/₁₀₀

= ⁸²³⁶⁰/₁₀₀ = 823.6

Thus, Sale Price (SP) at a profit of 16% = $823.6 Answer

Method (2) Algebraic Method

Finding the Sale Price (SP) to earn the given profit using the Algebraic Method when the Sale Pric (SP) at a loss percent is given

Given, the sale price (SP) = $589.3

And, the loss = 17%

Then, the Sale Price (SP) to earn a profit of 16% = ?

Let the Cost Price (CP) = m

Here given loss = 17%

Calculation of loss

loss is calculated on cost price (CP)

Formula to find the loss = loss% of CP

Thus, loss on the cost price of m

= 17% of m

= 17% × m

= ¹⁷/₁₀₀ × m

⇒ loss = ^{17 m}/₁₀₀

Calculation of Cost Price (CP)

The Sale Price (SP) = Cost Price (CP) – loss

⇒ 589.3 = m – ^{17 m}/₁₀₀

⇒ 589.3 = ^{100 m – 17 m}/₁₀₀

⇒ 589.3 = ^{83 m}/₁₀₀

After cross multiplication, we get

589.3 × 100 = 83 m

⇒ 83 m = 589.3 × 100

⇒ m = ^{589.3 × 100}/₈₃

⇒ m = ⁵⁸⁹³⁰/₈₃ = 710

⇒ m = 710

Thus, the Cost Price (CP) = $710

Finding the Sale Price (SP) when the Cost Price (CP) and profit percent are known

Now, here, Cost Price = 710

And, the profit = 16%

Thus, Sale Price (SP)

= Cost Price (CP) + 16% of Cost Price (CP)

= 710 + ¹⁶/₁₀₀ × 710

= 710 + ^{16 × 710}/₁₀₀

= 710 + ¹¹³⁶⁰/₁₀₀

= 710 + 113.6 = 823.6

Thus, Sale Price (SP) at a profit of 16% = $823.6 Answer

Method (3) Unitary Method

Finding the Sale Price (SP) to earn a given profit when the Sale price (SP) at a loss is given

Given, the sale price (SP) = $589.3

And, the loss = 17%

Then, the Sale Price (SP) to earn a profit of 16% = ?

Let, CP = 100

16% profit = 16% of CP

= 16% of 100 = 16

Thus, Sale Price to earn a profit of 16% = CP + 16

= 100 + 16 = 116

⇒ Sale Price to earn a profit of 16% = 116

17% loss = 17% of CP

= 17% of 100 = 17

Thus, Sale Price at a loss of 17% = CP – Loss

= 100 – 17 = 83

⇒ Sale Price at a loss of 17% = 83

∵ If the Sale Price is 83, then to earn a profit of 16% the Sale Price should be = 116

∴ If the Sale Price is 1, then to earn a profit of 16% the Sale Price should be

= ¹¹⁶/₈₃

∴ If the Sale Price is 589.3, then to earn a profit of 16% the Sale Price should be

= ¹¹⁶/₈₃ × 589.3

= ^{116 × 589.3}/₈₃

= ^68358.8/₈₃ = 823.6

Thus, Sale Price to get a profit of 16% = $823.6 Answer

Method (4) Shortcut Method

Shortcut Method to find the Sale Price at a given profit when Sale Price at a loss is given

Given, the sale price (SP) = $589.3

And, the loss = 17%

Then, the Sale Price (SP) to earn a profit of 16% = ?

Here, the Sale Price at a loss of 17 = $589.3

This means 83% of the Cost Price (CP) = 589.3

Therefore, 1% of the Cost Price (CP) = ^589.3/₈₃

Therefore, 100% of the Cost Price (CP)

= ^589.3/₈₃ × 100 = 710

Thus, the Cost Price (CP) = $710

Now, we need to find the Sale Price at a profit of 16%

Thus, Sale Price at a profit of 16%

= 116% of the Cost Price (CP)

= 116% of 710

= ¹¹⁶/₁₀₀ × 710 = 823.6

Thus, the Cost Price at a profit of 16% = $823.6 Answer

Similar Questions

(1) The cost price of an article is $15 and the sale price is $20, then find the profit and profit percent.

(2) Find the cost price, if a vendor gets a loss of 15% by selling some articles for $2388.50.

(3) Mr. Bob buys 40 articles for $1 and sells 39 articles for $1. Find the profit percent in this sale.

(4) If a peddler buys 46 articles for $1 and sells 45 articles for $1 then, find the earnings in percentage.

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

(6) Bill sold his secondhand motorcycle for $512.50. In this sale, he got a profit of 25%. For how much amount had he purchased the motorcycle?

(7) A street seller buys 8 articles for $1 and sells 7 articles for $1. Find the profit percent in this sale.

(8) If a seller bought 24 apples per $1 and sold them at a rate of 23 apples per $1, then what would his profit percent be?

(9) What is the cost price, if Mrs. Jill earns a profit of 200% by selling some items for $11730?

(10) William loses 71% by selling an article for $988.90. For how much should he sell it to get a profit of 70%?