Profit And Loss
Math MCQs

Question :    For how much should Mr. Bose sell his furniture to get a profit of 28%, if he loses 29% by selling it for $930.10?

Correct Answer  1676.8

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) = $930.1

And, the loss = 29%

Then, the Sale Price (SP) to earn a profit of 28% = ?

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 – 29} × 930.1

= ¹⁰⁰/₇₁ × 930.1

= ^{100 × 930.1}/₇₁

= ⁹³⁰¹⁰/₇₁ = 1310

Thus, the Cost Price (CP) = $1310

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

Here now, CP = $1310

And, profit = 28%

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 + 28}/₁₀₀ × 1310

= ¹²⁸/₁₀₀ × 1310

= ^{128 × 1310}/₁₀₀

= ¹⁶⁷⁶⁸⁰/₁₀₀ = 1676.8

Thus, Sale Price (SP) at a profit of 28% = $1676.8 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) = $930.1

And, the loss = 29%

Then, the Sale Price (SP) to earn a profit of 28% = ?

Let the Cost Price (CP) = m

Here given loss = 29%

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

= 29% of m

= 29% × m

= ²⁹/₁₀₀ × m

⇒ loss = ^{29 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 930.1 = m – ^{29 m}/₁₀₀

⇒ 930.1 = ^{100 m – 29 m}/₁₀₀

⇒ 930.1 = ^{71 m}/₁₀₀

After cross multiplication, we get

930.1 × 100 = 71 m

⇒ 71 m = 930.1 × 100

⇒ m = ^{930.1 × 100}/₇₁

⇒ m = ⁹³⁰¹⁰/₇₁ = 1310

⇒ m = 1310

Thus, the Cost Price (CP) = $1310

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

Now, here, Cost Price = 1310

And, the profit = 28%

Thus, Sale Price (SP)

= Cost Price (CP) + 28% of Cost Price (CP)

= 1310 + ²⁸/₁₀₀ × 1310

= 1310 + ^{28 × 1310}/₁₀₀

= 1310 + ³⁶⁶⁸⁰/₁₀₀

= 1310 + 366.8 = 1676.8

Thus, Sale Price (SP) at a profit of 28% = $1676.8 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) = $930.1

And, the loss = 29%

Then, the Sale Price (SP) to earn a profit of 28% = ?

Let, CP = 100

28% profit = 28% of CP

= 28% of 100 = 28

Thus, Sale Price to earn a profit of 28% = CP + 28

= 100 + 28 = 128

⇒ Sale Price to earn a profit of 28% = 128

29% loss = 29% of CP

= 29% of 100 = 29

Thus, Sale Price at a loss of 29% = CP – Loss

= 100 – 29 = 71

⇒ Sale Price at a loss of 29% = 71

∵ If the Sale Price is 71, then to earn a profit of 28% the Sale Price should be = 128

∴ If the Sale Price is 1, then to earn a profit of 28% the Sale Price should be

= ¹²⁸/₇₁

∴ If the Sale Price is 930.1, then to earn a profit of 28% the Sale Price should be

= ¹²⁸/₇₁ × 930.1

= ^{128 × 930.1}/₇₁

= ^119052.8/₇₁ = 1676.8

Thus, Sale Price to get a profit of 28% = $1676.8 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) = $930.1

And, the loss = 29%

Then, the Sale Price (SP) to earn a profit of 28% = ?

Here, the Sale Price at a loss of 29 = $930.1

This means 71% of the Cost Price (CP) = 930.1

Therefore, 1% of the Cost Price (CP) = ^930.1/₇₁

Therefore, 100% of the Cost Price (CP)

= ^930.1/₇₁ × 100 = 1310

Thus, the Cost Price (CP) = $1310

Now, we need to find the Sale Price at a profit of 28%

Thus, Sale Price at a profit of 28%

= 128% of the Cost Price (CP)

= 128% of 1310

= ¹²⁸/₁₀₀ × 1310 = 1676.8

Thus, the Cost Price at a profit of 28% = $1676.8 Answer

Similar Questions

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(2) 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.

(3) What was the cost price, if a trader gets a loss of 17% by selling an article for $2664.30?

(4) John loses 64% by selling an article for $1101.60. For how much should he sell it to get a profit of 63%?

(5) Mr. Steven loses 96% by selling an article for $186.40. For how much should he sell it to get a profit of 95%?

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

(7) If a trader gets a loss of 66% by selling ten TV sets for $4423.40 then find the cost price of all those TV sets

(8) If after selling 5 bags of rice for $1297.20 a shopkeeper gets a loss of 8% then what was the cost price of the rice?

(9) Mrs. Julie purchased 27 oranges for $1 and sold 26 oranges for $1. What will be his profit percentage?

(10) Mr. Robert sold his motorcycle for $1629 and got a loss of 10%. What was his cost price?