Profit And Loss
Math MCQs

Question :    Mr. Donald loses 85% by selling an article for $616.50. For how much should he sell it to get a profit of 84%?

Correct Answer  7562.4

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) = $616.5

And, the loss = 85%

Then, the Sale Price (SP) to earn a profit of 84% = ?

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 – 85} × 616.5

= ¹⁰⁰/₁₅ × 616.5

= ^{100 × 616.5}/₁₅

= ⁶¹⁶⁵⁰/₁₅ = 4110

Thus, the Cost Price (CP) = $4110

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

Here now, CP = $4110

And, profit = 84%

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 + 84}/₁₀₀ × 4110

= ¹⁸⁴/₁₀₀ × 4110

= ^{184 × 4110}/₁₀₀

= ⁷⁵⁶²⁴⁰/₁₀₀ = 7562.4

Thus, Sale Price (SP) at a profit of 84% = $7562.4 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) = $616.5

And, the loss = 85%

Then, the Sale Price (SP) to earn a profit of 84% = ?

Let the Cost Price (CP) = m

Here given loss = 85%

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

= 85% of m

= 85% × m

= ⁸⁵/₁₀₀ × m

⇒ loss = ^{85 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 616.5 = m – ^{85 m}/₁₀₀

⇒ 616.5 = ^{100 m – 85 m}/₁₀₀

⇒ 616.5 = ^{15 m}/₁₀₀

After cross multiplication, we get

616.5 × 100 = 15 m

⇒ 15 m = 616.5 × 100

⇒ m = ^{616.5 × 100}/₁₅

⇒ m = ⁶¹⁶⁵⁰/₁₅ = 4110

⇒ m = 4110

Thus, the Cost Price (CP) = $4110

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

Now, here, Cost Price = 4110

And, the profit = 84%

Thus, Sale Price (SP)

= Cost Price (CP) + 84% of Cost Price (CP)

= 4110 + ⁸⁴/₁₀₀ × 4110

= 4110 + ^{84 × 4110}/₁₀₀

= 4110 + ³⁴⁵²⁴⁰/₁₀₀

= 4110 + 3452.4 = 7562.4

Thus, Sale Price (SP) at a profit of 84% = $7562.4 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) = $616.5

And, the loss = 85%

Then, the Sale Price (SP) to earn a profit of 84% = ?

Let, CP = 100

84% profit = 84% of CP

= 84% of 100 = 84

Thus, Sale Price to earn a profit of 84% = CP + 84

= 100 + 84 = 184

⇒ Sale Price to earn a profit of 84% = 184

85% loss = 85% of CP

= 85% of 100 = 85

Thus, Sale Price at a loss of 85% = CP – Loss

= 100 – 85 = 15

⇒ Sale Price at a loss of 85% = 15

∵ If the Sale Price is 15, then to earn a profit of 84% the Sale Price should be = 184

∴ If the Sale Price is 1, then to earn a profit of 84% the Sale Price should be

= ¹⁸⁴/₁₅

∴ If the Sale Price is 616.5, then to earn a profit of 84% the Sale Price should be

= ¹⁸⁴/₁₅ × 616.5

= ^{184 × 616.5}/₁₅

= ¹¹³⁴³⁶/₁₅ = 7562.4

Thus, Sale Price to get a profit of 84% = $7562.4 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) = $616.5

And, the loss = 85%

Then, the Sale Price (SP) to earn a profit of 84% = ?

Here, the Sale Price at a loss of 85 = $616.5

This means 15% of the Cost Price (CP) = 616.5

Therefore, 1% of the Cost Price (CP) = ^616.5/₁₅

Therefore, 100% of the Cost Price (CP)

= ^616.5/₁₅ × 100 = 4110

Thus, the Cost Price (CP) = $4110

Now, we need to find the Sale Price at a profit of 84%

Thus, Sale Price at a profit of 84%

= 184% of the Cost Price (CP)

= 184% of 4110

= ¹⁸⁴/₁₀₀ × 4110 = 7562.4

Thus, the Cost Price at a profit of 84% = $7562.4 Answer

Similar Questions

(1) If a trader gets a loss of 72% by selling 15 bags of apples for $3978.80 then find the cost price of the apples.

(2) If a vendor gets a loss of 70% by selling ten bags of banana for $4143 then find the cost price of all those bananas.

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

(4) Find the cost price, if a trader gets a loss of 39% by selling 100 packets of fruits for $4642.10

(5) Find the cost price, if a dealer earns a profit of 245% by selling a plot for $16594.5

(6) If a vendor gets a loss of 21% by selling some apples for $3167.90 then what was the cost price of those apples?

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

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

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

(10) If a shopkeeper gets a loss of 65% by selling five TV sets for $4483.50 then find the cost price of all those TV sets.