Profit And Loss
Math MCQs

Question :    A trader loses 54% by selling an article for $1177.60. For how much should he sell it to get a profit of 53%?

Correct Answer  3916.8

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) = $1177.6

And, the loss = 54%

Then, the Sale Price (SP) to earn a profit of 53% = ?

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 – 54} × 1177.6

= ¹⁰⁰/₄₆ × 1177.6

= ^{100 × 1177.6}/₄₆

= ¹¹⁷⁷⁶⁰/₄₆ = 2560

Thus, the Cost Price (CP) = $2560

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

Here now, CP = $2560

And, profit = 53%

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 + 53}/₁₀₀ × 2560

= ¹⁵³/₁₀₀ × 2560

= ^{153 × 2560}/₁₀₀

= ³⁹¹⁶⁸⁰/₁₀₀ = 3916.8

Thus, Sale Price (SP) at a profit of 53% = $3916.8 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) = $1177.6

And, the loss = 54%

Then, the Sale Price (SP) to earn a profit of 53% = ?

Let the Cost Price (CP) = m

Here given loss = 54%

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

= 54% of m

= 54% × m

= ⁵⁴/₁₀₀ × m

⇒ loss = ^{54 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 1177.6 = m – ^{54 m}/₁₀₀

⇒ 1177.6 = ^{100 m – 54 m}/₁₀₀

⇒ 1177.6 = ^{46 m}/₁₀₀

After cross multiplication, we get

1177.6 × 100 = 46 m

⇒ 46 m = 1177.6 × 100

⇒ m = ^{1177.6 × 100}/₄₆

⇒ m = ¹¹⁷⁷⁶⁰/₄₆ = 2560

⇒ m = 2560

Thus, the Cost Price (CP) = $2560

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

Now, here, Cost Price = 2560

And, the profit = 53%

Thus, Sale Price (SP)

= Cost Price (CP) + 53% of Cost Price (CP)

= 2560 + ⁵³/₁₀₀ × 2560

= 2560 + ^{53 × 2560}/₁₀₀

= 2560 + ¹³⁵⁶⁸⁰/₁₀₀

= 2560 + 1356.8 = 3916.8

Thus, Sale Price (SP) at a profit of 53% = $3916.8 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) = $1177.6

And, the loss = 54%

Then, the Sale Price (SP) to earn a profit of 53% = ?

Let, CP = 100

53% profit = 53% of CP

= 53% of 100 = 53

Thus, Sale Price to earn a profit of 53% = CP + 53

= 100 + 53 = 153

⇒ Sale Price to earn a profit of 53% = 153

54% loss = 54% of CP

= 54% of 100 = 54

Thus, Sale Price at a loss of 54% = CP – Loss

= 100 – 54 = 46

⇒ Sale Price at a loss of 54% = 46

∵ If the Sale Price is 46, then to earn a profit of 53% the Sale Price should be = 153

∴ If the Sale Price is 1, then to earn a profit of 53% the Sale Price should be

= ¹⁵³/₄₆

∴ If the Sale Price is 1177.6, then to earn a profit of 53% the Sale Price should be

= ¹⁵³/₄₆ × 1177.6

= ^{153 × 1177.6}/₄₆

= ^180172.8/₄₆ = 3916.8

Thus, Sale Price to get a profit of 53% = $3916.8 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) = $1177.6

And, the loss = 54%

Then, the Sale Price (SP) to earn a profit of 53% = ?

Here, the Sale Price at a loss of 54 = $1177.6

This means 46% of the Cost Price (CP) = 1177.6

Therefore, 1% of the Cost Price (CP) = ^1177.6/₄₆

Therefore, 100% of the Cost Price (CP)

= ^1177.6/₄₆ × 100 = 2560

Thus, the Cost Price (CP) = $2560

Now, we need to find the Sale Price at a profit of 53%

Thus, Sale Price at a profit of 53%

= 153% of the Cost Price (CP)

= 153% of 2560

= ¹⁵³/₁₀₀ × 2560 = 3916.8

Thus, the Cost Price at a profit of 53% = $3916.8 Answer

Similar Questions

(1) Potter loses 90% by selling an article for $436. For how much should he sell it to get a profit of 89%?

(2) A shopkeeper loses 40% by selling an article for $1116.00. For how much should he sell it to get a profit of 39%?

(3) A shopkeeper earns a profit of 175% by selling some antique articles for $9377.50. What was the cost price of those antique articles?

(4) James loses 65% by selling an article for $1088.50. For how much should he sell it to get a profit of 64%?

(5) A dealer loses 21% by selling an article for $718.90. For how much should he sell it to get a profit of 20%?

(6) By selling some goods for $3249 a shopkeeper earns a profit of 90%. Find the cost price of those goods.

(7) Calculate the earnings percentage if a hawker buys 58 articles for $1 and sells 57 articles for $1.

(8) If a hawker bought 63 candies for $1 and sold them at a rate of 62 candies per $1 then, find the profit percent.

(9) Find the cost price, if a dealer gets a loss of 31% by selling 400 stocks for $4146.90

(10) If a hawker buys 75 refill for $1 and sold them at a rate of 74 per $1 then calculate his profit in percentage.