Profit And Loss
Math MCQs

Question :    Find the cost price, if a trader gets a loss of 48% by selling 500 kg of rice for $4893.20

Correct Answer  $9410

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) = $4893.2

And, the loss = 48%

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 – 48} × 4893.2

= ¹⁰⁰/₅₂ × 4893.2

= ⁴⁸⁹³²⁰/₅₂ = 9410

Thus, the Cost Price (CP) = $9410 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 = 48%

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

= 48% of m

= 48% × m

= ⁴⁸/₁₀₀ × m

⇒ loss = ^{48 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

⇒ 4893.2 = m – ^{48 m}/₁₀₀

⇒ 4893.2 = ^{100 m – 48 m}/₁₀₀

⇒ 4893.2 = ^{52 m}/₁₀₀

After cross multiplication, we get

4893.2 × 100 = 52 m

⇒ 52 m = 4893.2 × 100

⇒ m = ^{4893.2 × 100}/₅₂

⇒ m = ^{4893.2 × 100}/₅₂

⇒ m = ⁴⁸⁹³²⁰/₅₂ = 9410

Thus, the Cost Price (CP) = $9410 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) = $4893.2

And, the loss = 48%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 48% of 100 = 48

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

⇒ Sale Price (SP) = 100 – 48

⇒ Sale Price (SP) = 52

∵ If the Sale Price (SP) is 52, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₅₂

∴ If the Sale Price (SP) is 4893.2, then the Cost Price (CP)

= ¹⁰⁰/₅₂ × 4893.2

= ^{100 × 4893.2}/₅₂ = 9410

Thus, the Cost Price (CP) = $9410 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) = $4893.2

And, the loss = 48%

Then, the Cost Price (CP) = ?

SP = 52% of CP

⇒ SP = 52% of CP

⇒ 4893.2 = ⁵²/₁₀₀ × CP

⇒ 4893.2 = ^{52 CP}/₁₀₀

After cross multiplication

⇒ 4893.2 × 100 = 52 CP

⇒ 52 CP = 4893.2 × 100

⇒ CP = ^{4893.2 × 100}/₅₂

⇒ CP = ⁴⁸⁹³²⁰/₅₂ = 9410

⇒ CP = $9410 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 = 48%

And the Sale Price = $4893.2

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

⇒ 100 – 48% of the Cost Price = $4893.2

⇒ 52% of the Cost Price = 4893.2

Therefore, 1% of the Cost Price = ^4893.2/₅₂

Thus, 100% the Cost Price = ^4893.2/₅₂ × 100

= ⁴⁸⁹³²⁰/₅₂ = 9410

Thus the Cost Price (CP) = $9410 Answer

Similar Questions

(1) 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.

(2) How much percent will Peter earn if he buys 37 articles for $1 and sells 36 articles for $1?

(3) 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.

(4) Mr. Peter loses 44% by selling an article for $1153.60. For how much should he sell it to get a profit of 43%?

(5) A street seller buys 8 articles for $1 and sells 7 articles for $1. Find the profit percent in this sale.

(6) If a broker loses 39% by selling some of his stocks for $1104.10 then he should sell them for how much to get a profit of 38%?

(7) Find the earnings in percent if a vendor buys 43 articles for $1 and sells 42 articles for $1.

(8) If a shopkeeper gets a loss of 53% by selling 200 kg of rice for $4892.70 then find the cost price of rice.

(9) Mr. Oliver loses 34% by selling an article for $1029.60. For how much should he sell it to get a profit of 33%?

(10) A dealer loses 59% by selling an article for $1152.10. For how much should he sell it to get a profit of 58%?