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

(1) For how much Mr. Peter should sell his books to get a profit of 11%? If he loses 12% by selling them for $404.80.

(2) Find the cost price, if a trader gets a loss of 58% by selling two TV sets for $4792.20

(3) A dealer loses 56% by selling an article for $1170.40. For how much should he sell it to get a profit of 55%?

(4) After selling an article for $282.10, a shopkeeper gets a loss of 9%. Thus, to earn a profit of 8% he should sell it at which price?

(5) After selling some articles for $22269.00 a trader earns a profit of 290%. Find the cost price.

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

(7) John loses 63% by selling an article for $1113.70. For how much should he sell it to get a profit of 62%?

(8) If Robert purchased a TV set in an auction at $250 and sold it at $300, then calculate the profit earned and profit percent in this sale.

(9) If Noah buys 32 articles for $1 and sells them at a rate of 31 articles per $1 then, find his profit percent.

(10) Bill sold a bicycle for $840. If he purchased it at $600, then calculate his profit and profit percent in this sale.