Profit And Loss
Math MCQs

Question :    If a trader gets a loss of 24% by selling 500 shares for $3503.60 then find the cost price of those shares.

Correct Answer  $4610

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) = $3503.6

And, the loss = 24%

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 – 24} × 3503.6

= ¹⁰⁰/₇₆ × 3503.6

= ³⁵⁰³⁶⁰/₇₆ = 4610

Thus, the Cost Price (CP) = $4610 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 = 24%

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

= 24% of m

= 24% × m

= ²/₁₀₀ × m

⇒ loss = ^{24 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

⇒ 3503.6 = m – ^{24 m}/₁₀₀

⇒ 3503.6 = ^{100 m – 24 m}/₁₀₀

⇒ 3503.6 = ^{76 m}/₁₀₀

After cross multiplication, we get

3503.6 × 100 = 76 m

⇒ 76 m = 3503.6 × 100

⇒ m = ^{3503.6 × 100}/₇₆

⇒ m = ^{3503.6 × 100}/₇₆

⇒ m = ³⁵⁰³⁶⁰/₇₆ = 4610

Thus, the Cost Price (CP) = $4610 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) = $3503.6

And, the loss = 24%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 24% of 100 = 24

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

⇒ Sale Price (SP) = 100 – 24

⇒ Sale Price (SP) = 76

∵ If the Sale Price (SP) is 76, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₇₆

∴ If the Sale Price (SP) is 3503.6, then the Cost Price (CP)

= ¹⁰⁰/₇₆ × 3503.6

= ^{100 × 3503.6}/₇₆ = 4610

Thus, the Cost Price (CP) = $4610 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) = $3503.6

And, the loss = 24%

Then, the Cost Price (CP) = ?

SP = 76% of CP

⇒ SP = 76% of CP

⇒ 3503.6 = ⁷⁶/₁₀₀ × CP

⇒ 3503.6 = ^{76 CP}/₁₀₀

After cross multiplication

⇒ 3503.6 × 100 = 76 CP

⇒ 76 CP = 3503.6 × 100

⇒ CP = ^{3503.6 × 100}/₇₆

⇒ CP = ³⁵⁰³⁶⁰/₇₆ = 4610

⇒ CP = $4610 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 = 24%

And the Sale Price = $3503.6

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

⇒ 100 – 24% of the Cost Price = $3503.6

⇒ 76% of the Cost Price = 3503.6

Therefore, 1% of the Cost Price = ^3503.6/₇₆

Thus, 100% the Cost Price = ^3503.6/₇₆ × 100

= ³⁵⁰³⁶⁰/₇₆ = 4610

Thus the Cost Price (CP) = $4610 Answer

Similar Questions

(1) Bill sold his secondhand motorcycle for $512.50. In this sale, he got a profit of 25%. For how much amount had he purchased the motorcycle?

(2) If a hawker buys buys 61 oranges for $1 and sells them at a rate of 60 oranges per $1 then, find the profit percent.

(3) Find the cost price, if a trader gets a loss of 44% by selling 500 packets of fruits for $48210.60

(4) What will be the earnings in percent if a hawker buys 59 articles for $1 and sells 58 articles for $1?

(5) Find the cost price, if a vendor gets a loss of 56% by selling a TV set for $4844.40.

(6) Bill sold a bicycle for $640. If he purchased it at $800, then calculate his loss and loss percent in this sale.

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

(8) Mr. John earns a profit of 190% by selling a old car for $10759. For how much had he purchased that house?

(9) If Mr. Peter buys 17 apples for $1 and sells 16 apples for $1 then, find the profit percent in this sale.

(10) 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.