Profit And Loss
Math MCQs

Question :    What will be the cost price, if a trader gets a loss of 2% by selling an article for $205.80?

Correct Answer  $210

Solution & Explanation

Solution

Finding the cost price if the sale price and loss percent are known

The cost price (CP) can be found using the formula, algebraic method, shortcut method, and taking the cost price as 100, 200, 300, 400, 500, or whatever you want. Here the five methods to solve this problem have been given.

Method (1) Using Formula

Finding the cost price using the formula when the sale price and loss percent are known

Given, the sale price (SP) = $205.8

And, the loss = 2%

Then, the Cost Price (CP) = ?

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 – 2} × 205.8

= ¹⁰⁰/₉₈ × 205.8

= ²⁰⁵⁸⁰/₉₈ = 210

Thus, the Cost Price (CP) = $210 Answer

Method (2) Algebraic Method

Finding the cost price (CP) using the Algebraic Method when the Sale Price (SP) and the loss percent are given

Let the Cost Price (CP) = m

Here given loss = 2%

Calculation of loss

The loss and/or profit is calculated on the cost price (CP)

Formula to find the loss when the Cost Price and the Loss% are given

Loss = loss% of CP

Thus, loss on the cost price of m

= Loss% of m

= 2% of m

= 2% × m

= ²/₁₀₀ × m

⇒ loss = ^{2 m}/₁₀₀

Calculation of Cost Price (CP)

Formula to find the Sale Price (SP) when the Cost Price (CP) and the Loss are given

Sale Price (SP) = Cost Price (CP) – Loss

⇒ 205.8 = m – ^{2 m}/₁₀₀

⇒ 205.8 = ^{100 m – 2 m}/₁₀₀

⇒ 205.8 = ^{98 m}/₁₀₀

After cross multiplication, we get

205.8 × 100 = 98 m

⇒ 98 m = 205.8 × 100

⇒ m = ^{205.8 × 100}/₉₈

⇒ m = ^{205.8 × 100}/₉₈

⇒ m = ²⁰⁵⁸⁰/₉₈ = 210

Thus, the Cost Price (CP) = $210 Answer

Method (3) Unitary Method

Finding the cost price (CP) using Unitary Method by taking the cost price (CP) is equal to 100 when the SP and the loss percent are given

Given, the sale price (SP) = $205.8

And, the loss = 2%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 2% of 100 = 2

Thus, Sale Price (SP) = Cost Price (CP) – loss

⇒ Sale Price (SP) = 100 – 2

⇒ Sale Price (SP) = 98

∵ If the Sale Price (SP) is 98, then the Cost Price (CP) = 100

∴ If the Sale Price (SP) is 1, then the Cost Price (CP)

= ¹⁰⁰/₉₈

∴ If the Sale Price (SP) is 205.8, then the Cost Price (CP)

= ¹⁰⁰/₉₈ × 205.8

= ^{100 × 205.8}/₉₈ = 210

Thus, the Cost Price (CP) = $210 Answer

Method (4) Shortcut Method (1)

Shortcut Method to find Cost Price (CP) when SP and loss percent are known

Given, the sale price (SP) = $205.8

And, the loss = 2%

Then, the Cost Price (CP) = ?

SP = 98% of CP

⇒ SP = 98% of CP

⇒ 205.8 = ⁹⁸/₁₀₀ × CP

⇒ 205.8 = ^{98 CP}/₁₀₀

After cross multiplication

⇒ 205.8 × 100 = 98 CP

⇒ 98 CP = 205.8 × 100

⇒ CP = ^{205.8 × 100}/₉₈

⇒ CP = ²⁰⁵⁸⁰/₉₈ = 210

⇒ CP = $210 Answer

Method (5) Shortcut Method (2)

Shortcut Method (2) to find Cost Price (CP) when SP and loss percent are known

Here loss and the Sale Price are given and the Cost Price is to find

Here as given, the loss = 2%

And the Sale Price = $205.8

This means 100 – loss% of the Cost Price = Sale Price

⇒ 100 – 2% of the Cost Price = $205.8

⇒ 98% of the Cost Price = 205.8

Therefore, 1% of the Cost Price = ^205.8/₉₈

Thus, 100% the Cost Price = ^205.8/₉₈ × 100

= ²⁰⁵⁸⁰/₉₈ = 210

Thus the Cost Price (CP) = $210 Answer

Similar Questions

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(2) Mr. Bobby earns a profit of 120% by selling a TV set for $5082. What was the cost price of the TV set?

(3) Find the cost price, if a trader gets a loss of 50% by selling 500 bags of rice for $4905

(4) Mr. Donald loses 86% by selling an article for $582.40. For how much should he sell it to get a profit of 85%?

(5) Mrs. Mary loses 19% by selling an article for $656.10. For how much should she sell it to get a profit of 18%?

(6) How much percent will John get if he buys 39 articles for $1 and sells at a rate of 38 articles per $1?

(7) Mr. Donald loses 88% by selling an article for $511.20. For how much should he sell it to get a profit of 87%?

(8) 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.

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

(10) What will be the profit percentage if a hawker buys 64 articles for $1 and sells 63 articles for $1?