Profit And Loss
MCQs Math


Question:     A dealer loses 60% by selling an article for $1144.00. For how much should he sell it to get a profit of 59%?


Correct Answer  4547.4

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) = $1144

And, the loss = 60%

Then, the Sale Price (SP) to earn a profit of 59% = ?

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 – 60 × 1144

= 100/40 × 1144

= 100 × 1144/40

= 114400/40 = 2860

Thus, the Cost Price (CP) = $2860

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

Here now, CP = $2860

And, profit = 59%

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 + 59/100 × 2860

= 159/100 × 2860

= 159 × 2860/100

= 454740/100 = 4547.4

Thus, Sale Price (SP) at a profit of 59% = $4547.4 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) = $1144

And, the loss = 60%

Then, the Sale Price (SP) to earn a profit of 59% = ?

Let the Cost Price (CP) = m

Here given loss = 60%

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

= 60% of m

= 60% × m

= 60/100 × m

⇒ loss = 60 m/100

Calculation of Cost Price (CP)

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

⇒ 1144 = m – 60 m/100

⇒ 1144 = 100 m – 60 m/100

⇒ 1144 = 40 m/100

After cross multiplication, we get

1144 × 100 = 40 m

⇒ 40 m = 1144 × 100

⇒ m = 1144 × 100/40

⇒ m = 114400/40 = 2860

⇒ m = 2860

Thus, the Cost Price (CP) = $2860

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

Now, here, Cost Price = 2860

And, the profit = 59%

Thus, Sale Price (SP)

= Cost Price (CP) + 59% of Cost Price (CP)

= 2860 + 59/100 × 2860

= 2860 + 59 × 2860/100

= 2860 + 168740/100

= 2860 + 1687.4 = 4547.4

Thus, Sale Price (SP) at a profit of 59% = $4547.4 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) = $1144

And, the loss = 60%

Then, the Sale Price (SP) to earn a profit of 59% = ?

Let, CP = 100

59% profit = 59% of CP

= 59% of 100 = 59

Thus, Sale Price to earn a profit of 59% = CP + 59

= 100 + 59 = 159

⇒ Sale Price to earn a profit of 59% = 159

60% loss = 60% of CP

= 60% of 100 = 60

Thus, Sale Price at a loss of 60% = CP – Loss

= 100 – 60 = 40

⇒ Sale Price at a loss of 60% = 40

∵ If the Sale Price is 40, then to earn a profit of 59% the Sale Price should be = 159

∴ If the Sale Price is 1, then to earn a profit of 59% the Sale Price should be

= 159/40

∴ If the Sale Price is 1144, then to earn a profit of 59% the Sale Price should be

= 159/40 × 1144

= 159 × 1144/40

= 181896/40 = 4547.4

Thus, Sale Price to get a profit of 59% = $4547.4 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) = $1144

And, the loss = 60%

Then, the Sale Price (SP) to earn a profit of 59% = ?

Here, the Sale Price at a loss of 60 = $1144

This means 40% of the Cost Price (CP) = 1144

Therefore, 1% of the Cost Price (CP) = 1144/40

Therefore, 100% of the Cost Price (CP)

= 1144/40 × 100 = 2860

Thus, the Cost Price (CP) = $2860

Now, we need to find the Sale Price at a profit of 59%

Thus, Sale Price at a profit of 59%

= 159% of the Cost Price (CP)

= 159% of 2860

= 159/100 × 2860 = 4547.4

Thus, the Cost Price at a profit of 59% = $4547.4 Answer


Similar Questions

(1) If a hawker bought 22 apples per $1 and sold them at a rate of 21 apples per $1, then what would his profit percent be?

(2) If a book seller gets a loss of 33% by selling 300 books for $4294.70 then find the cost price of the books.

(3) By selling some items for $12741.00 a trader earns a profit of 210%. Find the cost price.

(4) A seller gets a profit of 7% by selling a TV set for $4280. If he would have sold it for $4200, then find his profit percent.

(5) Find the cost price, if a trader gets a loss of 59% by selling five TV sets for $4760.10

(6) 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.

(7) Find the cost price, if a share broker gets a loss of 27% by selling 200 shares for $3803.30.

(8) Mr. Joseph loses 5% by selling an article for $104.50. For how much should he sell it to get a profit of 4%?

(9) If a vendor bought 62 candies for $1 and sold 61 candies per $1 then find the profit percent.

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


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