Profit And Loss
Math MCQs

Question :    Find the cost price, if a trader gets a loss of 35% by selling some articles for $4426.50

Correct Answer  $6810

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) = $4426.5

And, the loss = 35%

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 – 35} × 4426.5

= ¹⁰⁰/₆₅ × 4426.5

= ⁴⁴²⁶⁵⁰/₆₅ = 6810

Thus, the Cost Price (CP) = $6810 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 = 35%

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

= 35% of m

= 35% × m

= ²/₁₀₀ × m

⇒ loss = ^{35 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

⇒ 4426.5 = m – ^{35 m}/₁₀₀

⇒ 4426.5 = ^{100 m – 35 m}/₁₀₀

⇒ 4426.5 = ^{65 m}/₁₀₀

After cross multiplication, we get

4426.5 × 100 = 65 m

⇒ 65 m = 4426.5 × 100

⇒ m = ^{4426.5 × 100}/₆₅

⇒ m = ^{4426.5 × 100}/₆₅

⇒ m = ⁴⁴²⁶⁵⁰/₆₅ = 6810

Thus, the Cost Price (CP) = $6810 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) = $4426.5

And, the loss = 35%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 35% of 100 = 35

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

⇒ Sale Price (SP) = 100 – 35

⇒ Sale Price (SP) = 65

∵ If the Sale Price (SP) is 65, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₆₅

∴ If the Sale Price (SP) is 4426.5, then the Cost Price (CP)

= ¹⁰⁰/₆₅ × 4426.5

= ^{100 × 4426.5}/₆₅ = 6810

Thus, the Cost Price (CP) = $6810 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) = $4426.5

And, the loss = 35%

Then, the Cost Price (CP) = ?

SP = 65% of CP

⇒ SP = 65% of CP

⇒ 4426.5 = ⁶⁵/₁₀₀ × CP

⇒ 4426.5 = ^{65 CP}/₁₀₀

After cross multiplication

⇒ 4426.5 × 100 = 65 CP

⇒ 65 CP = 4426.5 × 100

⇒ CP = ^{4426.5 × 100}/₆₅

⇒ CP = ⁴⁴²⁶⁵⁰/₆₅ = 6810

⇒ CP = $6810 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 = 35%

And the Sale Price = $4426.5

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

⇒ 100 – 35% of the Cost Price = $4426.5

⇒ 65% of the Cost Price = 4426.5

Therefore, 1% of the Cost Price = ^4426.5/₆₅

Thus, 100% the Cost Price = ^4426.5/₆₅ × 100

= ⁴⁴²⁶⁵⁰/₆₅ = 6810

Thus the Cost Price (CP) = $6810 Answer

Similar Questions

(1) Find the cost price, if a broker earns a profit of 385% by selling an article for $36908.5

(2) Find the cost price, if a trader gets a loss of 36% by selling 500 packets of fruits for $4486.40

(3) John sold rice at $7.20 per kg. If he purchased 120 kg of rice for $960, then calculate the loss and loss percent in this sale.

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

(5) If a trader gets a loss of 72% by selling 15 bags of apples for $3978.80 then find the cost price of the apples.

(6) If a seller bought 24 apples per $1 and sold them at a rate of 23 apples per $1, then what would his profit percent be?

(7) If a hawker bought 22 apples per $1 and sold them at a rate of 21 apples per $1, then what would his profit percent be?

(8) What will be profit percent if a peddler buys 12 kiwis for $1 and sells 11 kiwis for $1?

(9) Find the cost price, if Mrs. Julie earns a profit of 360% by selling some articles for $32706

(10) By selling some items for $1788.90 a vendor gets a loss of 11%. Find the cost price of those items.