Profit And Loss
Math MCQs

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

Correct Answer  $8610

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) = $4821.6

And, the loss = 44%

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 – 44} × 4821.6

= ¹⁰⁰/₅₆ × 4821.6

= ⁴⁸²¹⁶⁰/₅₆ = 8610

Thus, the Cost Price (CP) = $8610 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 = 44%

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

= 44% of m

= 44% × m

= ⁴⁴/₁₀₀ × m

⇒ loss = ^{44 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

⇒ 4821.6 = m – ^{44 m}/₁₀₀

⇒ 4821.6 = ^{100 m – 44 m}/₁₀₀

⇒ 4821.6 = ^{56 m}/₁₀₀

After cross multiplication, we get

4821.6 × 100 = 56 m

⇒ 56 m = 4821.6 × 100

⇒ m = ^{4821.6 × 100}/₅₆

⇒ m = ^{4821.6 × 100}/₅₆

⇒ m = ⁴⁸²¹⁶⁰/₅₆ = 8610

Thus, the Cost Price (CP) = $8610 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) = $4821.6

And, the loss = 44%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 44% of 100 = 44

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

⇒ Sale Price (SP) = 100 – 44

⇒ Sale Price (SP) = 56

∵ If the Sale Price (SP) is 56, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₅₆

∴ If the Sale Price (SP) is 4821.6, then the Cost Price (CP)

= ¹⁰⁰/₅₆ × 4821.6

= ^{100 × 4821.6}/₅₆ = 8610

Thus, the Cost Price (CP) = $8610 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) = $4821.6

And, the loss = 44%

Then, the Cost Price (CP) = ?

SP = 56% of CP

⇒ SP = 56% of CP

⇒ 4821.6 = ⁵⁶/₁₀₀ × CP

⇒ 4821.6 = ^{56 CP}/₁₀₀

After cross multiplication

⇒ 4821.6 × 100 = 56 CP

⇒ 56 CP = 4821.6 × 100

⇒ CP = ^{4821.6 × 100}/₅₆

⇒ CP = ⁴⁸²¹⁶⁰/₅₆ = 8610

⇒ CP = $8610 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 = 44%

And the Sale Price = $4821.6

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

⇒ 100 – 44% of the Cost Price = $4821.6

⇒ 56% of the Cost Price = 4821.6

Therefore, 1% of the Cost Price = ^4821.6/₅₆

Thus, 100% the Cost Price = ^4821.6/₅₆ × 100

= ⁴⁸²¹⁶⁰/₅₆ = 8610

Thus the Cost Price (CP) = $8610 Answer

Similar Questions

(1) A broker loses 41% by selling an article for $1126.90. For how much should he sell it to get a profit of 40%?

(2) Find the earnings percentage if a peddler buys 51 articles for $1 and sells 50 articles for $1.

(3) Calculate the earnings percentage if a vendor buys 56 articles for $1 and sells 55 articles for $1.

(4) A dealer earns a profit of 285% by selling some items for $21598.50. What was his cost price?

(5) Mrs. Mary earns a profit of 230% after selling an article for $14883. Find the cost price.

(6) How much percent will a hawker earn, if he buys 34 articles for $1 and sells 33 articles for $1?

(7) Mollie purchased 150 kg of wheat at $1350. Due to some unavoidable circumstances, he had to sell the wheat at $7.20 per kg. Calculate his total loss and loss percent in this sale.

(8) 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.

(9) If a trader gets a loss of 20% by selling some apples for $3048, then find the cost price of those apples.

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