Profit And Loss
Math MCQs

Question :    For how much should he sell the bicycle to get a profit of 19%, if a shopkeeper loses 20% by selling it for $688?

Correct Answer  1023.4

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) = $688

And, the loss = 20%

Then, the Sale Price (SP) to earn a profit of 19% = ?

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 – 20} × 688

= ¹⁰⁰/₈₀ × 688

= ^{100 × 688}/₈₀

= ⁶⁸⁸⁰⁰/₈₀ = 860

Thus, the Cost Price (CP) = $860

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

Here now, CP = $860

And, profit = 19%

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 + 19}/₁₀₀ × 860

= ¹¹⁹/₁₀₀ × 860

= ^{119 × 860}/₁₀₀

= ¹⁰²³⁴⁰/₁₀₀ = 1023.4

Thus, Sale Price (SP) at a profit of 19% = $1023.4 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) = $688

And, the loss = 20%

Then, the Sale Price (SP) to earn a profit of 19% = ?

Let the Cost Price (CP) = m

Here given loss = 20%

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

= 20% of m

= 20% × m

= ²⁰/₁₀₀ × m

⇒ loss = ^{20 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 688 = m – ^{20 m}/₁₀₀

⇒ 688 = ^{100 m – 20 m}/₁₀₀

⇒ 688 = ^{80 m}/₁₀₀

After cross multiplication, we get

688 × 100 = 80 m

⇒ 80 m = 688 × 100

⇒ m = ^{688 × 100}/₈₀

⇒ m = ⁶⁸⁸⁰⁰/₈₀ = 860

⇒ m = 860

Thus, the Cost Price (CP) = $860

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

Now, here, Cost Price = 860

And, the profit = 19%

Thus, Sale Price (SP)

= Cost Price (CP) + 19% of Cost Price (CP)

= 860 + ¹⁹/₁₀₀ × 860

= 860 + ^{19 × 860}/₁₀₀

= 860 + ¹⁶³⁴⁰/₁₀₀

= 860 + 163.4 = 1023.4

Thus, Sale Price (SP) at a profit of 19% = $1023.4 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) = $688

And, the loss = 20%

Then, the Sale Price (SP) to earn a profit of 19% = ?

Let, CP = 100

19% profit = 19% of CP

= 19% of 100 = 19

Thus, Sale Price to earn a profit of 19% = CP + 19

= 100 + 19 = 119

⇒ Sale Price to earn a profit of 19% = 119

20% loss = 20% of CP

= 20% of 100 = 20

Thus, Sale Price at a loss of 20% = CP – Loss

= 100 – 20 = 80

⇒ Sale Price at a loss of 20% = 80

∵ If the Sale Price is 80, then to earn a profit of 19% the Sale Price should be = 119

∴ If the Sale Price is 1, then to earn a profit of 19% the Sale Price should be

= ¹¹⁹/₈₀

∴ If the Sale Price is 688, then to earn a profit of 19% the Sale Price should be

= ¹¹⁹/₈₀ × 688

= ^{119 × 688}/₈₀

= ⁸¹⁸⁷²/₈₀ = 1023.4

Thus, Sale Price to get a profit of 19% = $1023.4 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) = $688

And, the loss = 20%

Then, the Sale Price (SP) to earn a profit of 19% = ?

Here, the Sale Price at a loss of 20 = $688

This means 80% of the Cost Price (CP) = 688

Therefore, 1% of the Cost Price (CP) = ⁶⁸⁸/₈₀

Therefore, 100% of the Cost Price (CP)

= ⁶⁸⁸/₈₀ × 100 = 860

Thus, the Cost Price (CP) = $860

Now, we need to find the Sale Price at a profit of 19%

Thus, Sale Price at a profit of 19%

= 119% of the Cost Price (CP)

= 119% of 860

= ¹¹⁹/₁₀₀ × 860 = 1023.4

Thus, the Cost Price at a profit of 19% = $1023.4 Answer

Similar Questions

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(2) If a broker gets a loss of 22% by selling 100 shares for $3283.80, then find the cost price of those shares.

(3) A shopkeeper earns 130% after selling some old bikes for $5773. What was his cost price?

(4) By selling a house for $14332.50, a dealer earns a profit of 225%. Find the cost price

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(7) Find the cost price, if a trader gets a loss of 12% by selling some of his stock of fruits for $1944.80. Find the cost price of those stock.

(8) William loses 72% by selling an article for $968.80. For how much should he sell it to get a profit of 71%?

(9) If Mr. Jobby buys 18 kiwis for $1 and sells them at a rate of 17 per $1 then what would be the profit percent?.

(10) After selling a furniture for $481.60 a shopkeeper gets a loss of 14%. In order to get a profit of 13% he should sell in for how much?