Profit And Loss
MCQs Math


Question:     Potter loses 91% by selling an article for $396.90. For how much should he sell it to get a profit of 90%?


Correct Answer  8379

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) = $396.9

And, the loss = 91%

Then, the Sale Price (SP) to earn a profit of 90% = ?

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 – 91 × 396.9

= 100/9 × 396.9

= 100 × 396.9/9

= 39690/9 = 4410

Thus, the Cost Price (CP) = $4410

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

Here now, CP = $4410

And, profit = 90%

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 + 90/100 × 4410

= 190/100 × 4410

= 190 × 4410/100

= 837900/100 = 8379

Thus, Sale Price (SP) at a profit of 90% = $8379 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) = $396.9

And, the loss = 91%

Then, the Sale Price (SP) to earn a profit of 90% = ?

Let the Cost Price (CP) = m

Here given loss = 91%

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

= 91% of m

= 91% × m

= 91/100 × m

⇒ loss = 91 m/100

Calculation of Cost Price (CP)

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

⇒ 396.9 = m – 91 m/100

⇒ 396.9 = 100 m – 91 m/100

⇒ 396.9 = 9 m/100

After cross multiplication, we get

396.9 × 100 = 9 m

⇒ 9 m = 396.9 × 100

⇒ m = 396.9 × 100/9

⇒ m = 39690/9 = 4410

⇒ m = 4410

Thus, the Cost Price (CP) = $4410

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

Now, here, Cost Price = 4410

And, the profit = 90%

Thus, Sale Price (SP)

= Cost Price (CP) + 90% of Cost Price (CP)

= 4410 + 90/100 × 4410

= 4410 + 90 × 4410/100

= 4410 + 396900/100

= 4410 + 3969 = 8379

Thus, Sale Price (SP) at a profit of 90% = $8379 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) = $396.9

And, the loss = 91%

Then, the Sale Price (SP) to earn a profit of 90% = ?

Let, CP = 100

90% profit = 90% of CP

= 90% of 100 = 90

Thus, Sale Price to earn a profit of 90% = CP + 90

= 100 + 90 = 190

⇒ Sale Price to earn a profit of 90% = 190

91% loss = 91% of CP

= 91% of 100 = 91

Thus, Sale Price at a loss of 91% = CP – Loss

= 100 – 91 = 9

⇒ Sale Price at a loss of 91% = 9

∵ If the Sale Price is 9, then to earn a profit of 90% the Sale Price should be = 190

∴ If the Sale Price is 1, then to earn a profit of 90% the Sale Price should be

= 190/9

∴ If the Sale Price is 396.9, then to earn a profit of 90% the Sale Price should be

= 190/9 × 396.9

= 190 × 396.9/9

= 75411/9 = 8379

Thus, Sale Price to get a profit of 90% = $8379 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) = $396.9

And, the loss = 91%

Then, the Sale Price (SP) to earn a profit of 90% = ?

Here, the Sale Price at a loss of 91 = $396.9

This means 9% of the Cost Price (CP) = 396.9

Therefore, 1% of the Cost Price (CP) = 396.9/9

Therefore, 100% of the Cost Price (CP)

= 396.9/9 × 100 = 4410

Thus, the Cost Price (CP) = $4410

Now, we need to find the Sale Price at a profit of 90%

Thus, Sale Price at a profit of 90%

= 190% of the Cost Price (CP)

= 190% of 4410

= 190/100 × 4410 = 8379

Thus, the Cost Price at a profit of 90% = $8379 Answer


Similar Questions

(1) A dealer gets a loss of 7% by selling an article for $195.30 then, for how much should he sell it to get a profit of 6%?

(2) If a vendor bought 20 apples per $1 and sold them at a rate of 19 apples per $1, then what would his profit percent be?

(3) Find the cost price, if a trader gets a loss of 67% by selling ten bags of apple for $4359.30

(4) if a vendor bought 74 nibs for $1 and sells them at a rate of 73 per $1 then calculate the profit in percent.

(5) Find the earnings percentage if a vendor buys 49 articles for $1 and sells 48 articles for $1.

(6) If a vendor purchased 73 coins for $1 and sells 72 coins for $1 then, find profit in percent.

(7) A shopkeeper gets a loss of 5% by selling some fruits for $769.50. Find the cost price of the furits.

(8) Mr. Henry loses 26% by selling an article for $858.4. For how much should he sell it to get a profit of 25%?

(9) Calculate the earnings in percent if a vendor buys 72 coins for $1 and sells 71 coins for $1.

(10) William loses 43% by selling an article for $1145.70. For how much should he sell it to get a profit of 42%?


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