Profit And Loss
MCQs Math


Question:     A dealer loses 28% by selling some articles for $907.20. For how much should he sell them to get a profit of 27%?


Correct Answer  1600.2

Solution And 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) = $907.2

And, the loss = 28%

Then, the Sale Price (SP) to earn a profit of 27% = ?

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 – 28 × 907.2

= 100/72 × 907.2

= 100 × 907.2/72

= 90720/72 = 1260

Thus, the Cost Price (CP) = $1260

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

Here now, CP = $1260

And, profit = 27%

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 + 27/100 × 1260

= 127/100 × 1260

= 127 × 1260/100

= 160020/100 = 1600.2

Thus, Sale Price (SP) at a profit of 27% = $1600.2 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) = $907.2

And, the loss = 28%

Then, the Sale Price (SP) to earn a profit of 27% = ?

Let the Cost Price (CP) = m

Here given loss = 28%

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

= 28% of m

= 28% × m

= 28/100 × m

⇒ loss = 28 m/100

Calculation of Cost Price (CP)

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

⇒ 907.2 = m – 28 m/100

⇒ 907.2 = 100 m – 28 m/100

⇒ 907.2 = 72 m/100

After cross multiplication, we get

907.2 × 100 = 72 m

⇒ 72 m = 907.2 × 100

⇒ m = 907.2 × 100/72

⇒ m = 90720/72 = 1260

⇒ m = 1260

Thus, the Cost Price (CP) = $1260

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

Now, here, Cost Price = 1260

And, the profit = 27%

Thus, Sale Price (SP)

= Cost Price (CP) + 27% of Cost Price (CP)

= 1260 + 27/100 × 1260

= 1260 + 27 × 1260/100

= 1260 + 34020/100

= 1260 + 340.2 = 1600.2

Thus, Sale Price (SP) at a profit of 27% = $1600.2 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) = $907.2

And, the loss = 28%

Then, the Sale Price (SP) to earn a profit of 27% = ?

Let, CP = 100

27% profit = 27% of CP

= 27% of 100 = 27

Thus, Sale Price to earn a profit of 27% = CP + 27

= 100 + 27 = 127

⇒ Sale Price to earn a profit of 27% = 127

28% loss = 28% of CP

= 28% of 100 = 28

Thus, Sale Price at a loss of 28% = CP – Loss

= 100 – 28 = 72

⇒ Sale Price at a loss of 28% = 72

∵ If the Sale Price is 72, then to earn a profit of 27% the Sale Price should be = 127

∴ If the Sale Price is 1, then to earn a profit of 27% the Sale Price should be

= 127/72

∴ If the Sale Price is 907.2, then to earn a profit of 27% the Sale Price should be

= 127/72 × 907.2

= 127 × 907.2/72

= 115214.4/72 = 1600.2

Thus, Sale Price to get a profit of 27% = $1600.2 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) = $907.2

And, the loss = 28%

Then, the Sale Price (SP) to earn a profit of 27% = ?

Here, the Sale Price at a loss of 28 = $907.2

This means 72% of the Cost Price (CP) = 907.2

Therefore, 1% of the Cost Price (CP) = 907.2/72

Therefore, 100% of the Cost Price (CP)

= 907.2/72 × 100 = 1260

Thus, the Cost Price (CP) = $1260

Now, we need to find the Sale Price at a profit of 27%

Thus, Sale Price at a profit of 27%

= 127% of the Cost Price (CP)

= 127% of 1260

= 127/100 × 1260 = 1600.2

Thus, the Cost Price at a profit of 27% = $1600.2 Answer


Similar Questions

(1) Find the cost price, if a trader gets a loss of 57% by selling a TV set for $4820.30

(2) 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?

(3) Find the cost price, if a trader earns a profit of 5% by selling an article for $10.5

(4) What will be the profit percentage if a hawker buys 64 articles for $1 and sells 63 articles for $1?

(5) A trader loses 42% by selling an article for $1136.80. For how much should he sell it to get a profit of 41%?

(6) Mr. John sold his scoory for $1465.10 and got a loss of 9%. What was the cost price of the scooty?

(7) Find the cost price, if a trader gets a loss of 38% by selling 600 packets of fruits for $4594.20

(8) For how much had Mr. Robert purchased his motorcycle if he earns a profit of 60% by selling it for $1776?

(9) Find the profit in percent if a vendor buys 65 articles for $1 and sells 64 articles for $1.

(10) A trader loses 47% by selling an article for $1171.30. For how much should he sell it to get a profit of 46%?


NCERT Solution and CBSE Notes for class twelve, eleventh, tenth, ninth, seventh, sixth, fifth, fourth and General Math for competitive Exams. ©