Profit And Loss
Math MCQs

Question :    A trader loses 52% by selling an article for $1180.80. For how much should he sell it to get a profit of 51%?

Correct Answer  3714.6

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) = $1180.8

And, the loss = 52%

Then, the Sale Price (SP) to earn a profit of 51% = ?

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 – 52} × 1180.8

= ¹⁰⁰/₄₈ × 1180.8

= ^{100 × 1180.8}/₄₈

= ¹¹⁸⁰⁸⁰/₄₈ = 2460

Thus, the Cost Price (CP) = $2460

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

Here now, CP = $2460

And, profit = 51%

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 + 51}/₁₀₀ × 2460

= ¹⁵¹/₁₀₀ × 2460

= ^{151 × 2460}/₁₀₀

= ³⁷¹⁴⁶⁰/₁₀₀ = 3714.6

Thus, Sale Price (SP) at a profit of 51% = $3714.6 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) = $1180.8

And, the loss = 52%

Then, the Sale Price (SP) to earn a profit of 51% = ?

Let the Cost Price (CP) = m

Here given loss = 52%

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

= 52% of m

= 52% × m

= ⁵²/₁₀₀ × m

⇒ loss = ^{52 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 1180.8 = m – ^{52 m}/₁₀₀

⇒ 1180.8 = ^{100 m – 52 m}/₁₀₀

⇒ 1180.8 = ^{48 m}/₁₀₀

After cross multiplication, we get

1180.8 × 100 = 48 m

⇒ 48 m = 1180.8 × 100

⇒ m = ^{1180.8 × 100}/₄₈

⇒ m = ¹¹⁸⁰⁸⁰/₄₈ = 2460

⇒ m = 2460

Thus, the Cost Price (CP) = $2460

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

Now, here, Cost Price = 2460

And, the profit = 51%

Thus, Sale Price (SP)

= Cost Price (CP) + 51% of Cost Price (CP)

= 2460 + ⁵¹/₁₀₀ × 2460

= 2460 + ^{51 × 2460}/₁₀₀

= 2460 + ¹²⁵⁴⁶⁰/₁₀₀

= 2460 + 1254.6 = 3714.6

Thus, Sale Price (SP) at a profit of 51% = $3714.6 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) = $1180.8

And, the loss = 52%

Then, the Sale Price (SP) to earn a profit of 51% = ?

Let, CP = 100

51% profit = 51% of CP

= 51% of 100 = 51

Thus, Sale Price to earn a profit of 51% = CP + 51

= 100 + 51 = 151

⇒ Sale Price to earn a profit of 51% = 151

52% loss = 52% of CP

= 52% of 100 = 52

Thus, Sale Price at a loss of 52% = CP – Loss

= 100 – 52 = 48

⇒ Sale Price at a loss of 52% = 48

∵ If the Sale Price is 48, then to earn a profit of 51% the Sale Price should be = 151

∴ If the Sale Price is 1, then to earn a profit of 51% the Sale Price should be

= ¹⁵¹/₄₈

∴ If the Sale Price is 1180.8, then to earn a profit of 51% the Sale Price should be

= ¹⁵¹/₄₈ × 1180.8

= ^{151 × 1180.8}/₄₈

= ^178300.8/₄₈ = 3714.6

Thus, Sale Price to get a profit of 51% = $3714.6 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) = $1180.8

And, the loss = 52%

Then, the Sale Price (SP) to earn a profit of 51% = ?

Here, the Sale Price at a loss of 52 = $1180.8

This means 48% of the Cost Price (CP) = 1180.8

Therefore, 1% of the Cost Price (CP) = ^1180.8/₄₈

Therefore, 100% of the Cost Price (CP)

= ^1180.8/₄₈ × 100 = 2460

Thus, the Cost Price (CP) = $2460

Now, we need to find the Sale Price at a profit of 51%

Thus, Sale Price at a profit of 51%

= 151% of the Cost Price (CP)

= 151% of 2460

= ¹⁵¹/₁₀₀ × 2460 = 3714.6

Thus, the Cost Price at a profit of 51% = $3714.6 Answer

Similar Questions

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(2) What was the cost price, if a trader gets a loss of 18% by selling some articles for $2796.20?

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

(4) Mr. Bob buys 40 articles for $1 and sells 39 articles for $1. Find the profit percent in this sale.

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

(6) If a dealer earns a profit of 255% by selling some articles for $17785.50, then find the cost price.

(7) Mike sold his car at a profit of 25%. If he purchased that car at $2500 then find the sale price of the car.

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

(9) Find the cost price, if a dealer earns a profit of 305% by selling a plot for $24340.50

(10) John purchased a bike for $500 and he sold it at a gain of 12%. Find the sale price of the bike.