Profit And Loss
Math MCQs

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

Correct Answer  $6010

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) = $4146.9

And, the loss = 31%

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 – 31} × 4146.9

= ¹⁰⁰/₆₉ × 4146.9

= ⁴¹⁴⁶⁹⁰/₆₉ = 6010

Thus, the Cost Price (CP) = $6010 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 = 31%

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

= 31% of m

= 31% × m

= ²/₁₀₀ × m

⇒ loss = ^{31 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

⇒ 4146.9 = m – ^{31 m}/₁₀₀

⇒ 4146.9 = ^{100 m – 31 m}/₁₀₀

⇒ 4146.9 = ^{69 m}/₁₀₀

After cross multiplication, we get

4146.9 × 100 = 69 m

⇒ 69 m = 4146.9 × 100

⇒ m = ^{4146.9 × 100}/₆₉

⇒ m = ^{4146.9 × 100}/₆₉

⇒ m = ⁴¹⁴⁶⁹⁰/₆₉ = 6010

Thus, the Cost Price (CP) = $6010 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) = $4146.9

And, the loss = 31%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 31% of 100 = 31

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

⇒ Sale Price (SP) = 100 – 31

⇒ Sale Price (SP) = 69

∵ If the Sale Price (SP) is 69, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₆₉

∴ If the Sale Price (SP) is 4146.9, then the Cost Price (CP)

= ¹⁰⁰/₆₉ × 4146.9

= ^{100 × 4146.9}/₆₉ = 6010

Thus, the Cost Price (CP) = $6010 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) = $4146.9

And, the loss = 31%

Then, the Cost Price (CP) = ?

SP = 69% of CP

⇒ SP = 69% of CP

⇒ 4146.9 = ⁶⁹/₁₀₀ × CP

⇒ 4146.9 = ^{69 CP}/₁₀₀

After cross multiplication

⇒ 4146.9 × 100 = 69 CP

⇒ 69 CP = 4146.9 × 100

⇒ CP = ^{4146.9 × 100}/₆₉

⇒ CP = ⁴¹⁴⁶⁹⁰/₆₉ = 6010

⇒ CP = $6010 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 = 31%

And the Sale Price = $4146.9

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

⇒ 100 – 31% of the Cost Price = $4146.9

⇒ 69% of the Cost Price = 4146.9

Therefore, 1% of the Cost Price = ^4146.9/₆₉

Thus, 100% the Cost Price = ^4146.9/₆₉ × 100

= ⁴¹⁴⁶⁹⁰/₆₉ = 6010

Thus the Cost Price (CP) = $6010 Answer

Similar Questions

(1) If a book seller gets a loss of 33% by selling 300 books for $4294.70 then find the cost price of the books.

(2) William loses 72% by selling an article for $968.80. For how much should he sell it to get a profit of 71%?

(3) If a trader gets a loss of 16% by selling some articles for $2528.40 then find the cost price.

(4) Mr. Steven loses 96% by selling an article for $186.40. For how much should he sell it to get a profit of 95%?

(5) Find the cost price, if a share broker gets a loss of 29% by selling 500 stocks for $3983.10

(6) Mr. Jack buys 13 articles for $1 and sells 12 articles for $1. Find his profit percent.

(7) If a trader earns a profit of 45% by selling an article for $1174.5, then find the cost price.

(8) What will be the profit in percent if a vendor buys 70 paper clips for $1 and sells at a rate of 69 per $1?

(9) Find the earnings percentage if a hawker buys 50 articles for $1 and sells 49 articles for $1.

(10) After selling some articles for $13261.50, a trader earns a profit of 215%. Find the cost price.