Profit And Loss
Math MCQs

Question :    For how much should a trader sell an item to get a profit of 49% if he loses 50% by selling it for $1180.00?

Correct Answer  3516.4

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) = $1180

And, the loss = 50%

Then, the Sale Price (SP) to earn a profit of 49% = ?

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 – 50} × 1180

= ¹⁰⁰/₅₀ × 1180

= ^{100 × 1180}/₅₀

= ¹¹⁸⁰⁰⁰/₅₀ = 2360

Thus, the Cost Price (CP) = $2360

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

Here now, CP = $2360

And, profit = 49%

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 + 49}/₁₀₀ × 2360

= ¹⁴⁹/₁₀₀ × 2360

= ^{149 × 2360}/₁₀₀

= ³⁵¹⁶⁴⁰/₁₀₀ = 3516.4

Thus, Sale Price (SP) at a profit of 49% = $3516.4 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) = $1180

And, the loss = 50%

Then, the Sale Price (SP) to earn a profit of 49% = ?

Let the Cost Price (CP) = m

Here given loss = 50%

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

= 50% of m

= 50% × m

= ⁵⁰/₁₀₀ × m

⇒ loss = ^{50 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 1180 = m – ^{50 m}/₁₀₀

⇒ 1180 = ^{100 m – 50 m}/₁₀₀

⇒ 1180 = ^{50 m}/₁₀₀

After cross multiplication, we get

1180 × 100 = 50 m

⇒ 50 m = 1180 × 100

⇒ m = ^{1180 × 100}/₅₀

⇒ m = ¹¹⁸⁰⁰⁰/₅₀ = 2360

⇒ m = 2360

Thus, the Cost Price (CP) = $2360

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

Now, here, Cost Price = 2360

And, the profit = 49%

Thus, Sale Price (SP)

= Cost Price (CP) + 49% of Cost Price (CP)

= 2360 + ⁴⁹/₁₀₀ × 2360

= 2360 + ^{49 × 2360}/₁₀₀

= 2360 + ¹¹⁵⁶⁴⁰/₁₀₀

= 2360 + 1156.4 = 3516.4

Thus, Sale Price (SP) at a profit of 49% = $3516.4 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) = $1180

And, the loss = 50%

Then, the Sale Price (SP) to earn a profit of 49% = ?

Let, CP = 100

49% profit = 49% of CP

= 49% of 100 = 49

Thus, Sale Price to earn a profit of 49% = CP + 49

= 100 + 49 = 149

⇒ Sale Price to earn a profit of 49% = 149

50% loss = 50% of CP

= 50% of 100 = 50

Thus, Sale Price at a loss of 50% = CP – Loss

= 100 – 50 = 50

⇒ Sale Price at a loss of 50% = 50

∵ If the Sale Price is 50, then to earn a profit of 49% the Sale Price should be = 149

∴ If the Sale Price is 1, then to earn a profit of 49% the Sale Price should be

= ¹⁴⁹/₅₀

∴ If the Sale Price is 1180, then to earn a profit of 49% the Sale Price should be

= ¹⁴⁹/₅₀ × 1180

= ^{149 × 1180}/₅₀

= ¹⁷⁵⁸²⁰/₅₀ = 3516.4

Thus, Sale Price to get a profit of 49% = $3516.4 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) = $1180

And, the loss = 50%

Then, the Sale Price (SP) to earn a profit of 49% = ?

Here, the Sale Price at a loss of 50 = $1180

This means 50% of the Cost Price (CP) = 1180

Therefore, 1% of the Cost Price (CP) = ¹¹⁸⁰/₅₀

Therefore, 100% of the Cost Price (CP)

= ¹¹⁸⁰/₅₀ × 100 = 2360

Thus, the Cost Price (CP) = $2360

Now, we need to find the Sale Price at a profit of 49%

Thus, Sale Price at a profit of 49%

= 149% of the Cost Price (CP)

= 149% of 2360

= ¹⁴⁹/₁₀₀ × 2360 = 3516.4

Thus, the Cost Price at a profit of 49% = $3516.4 Answer

Similar Questions

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(2) Find the cost price, if a share broker gets a loss of 26% by selling 100 shares for $3707.40.

(3) John gets a 20% profit after selling his laptop for $372. What was the cost price of the laptop?

(4) On a closing day, a shopkeeper earns a profit of 65%. If gets $1996.5 in total, then what was his cost price?

(5) A broker earns a profit of 310% by selling a house for $25051. Find the cost price.

(6) Mrs. John earned a profit of 330% by selling her car. If she sold her car for $27993, then find the cost price of the car.

(7) Noah loses 76% by selling an article for $878.40. For how much should he sell it to get a profit of 75%?

(8) How much percent will a vendor earn, if he buys 35 articles for $1 and sells 34 articles for $1?

(9) How much Mr. Gates had to pay to purchase his motorbike? If he gets a profit of 70% after selling it for $2227.

(10) The cost price of an article is $12, and the sale price is $15. Find the profit and profit percent.