Profit And Loss
Math MCQs

Question :    Find the cost price, if a trader gets a loss of 49% by selling 1500 kg rice for $4901.10

Correct Answer  $9610

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) = $4901.1

And, the loss = 49%

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 – 49} × 4901.1

= ¹⁰⁰/₅₁ × 4901.1

= ⁴⁹⁰¹¹⁰/₅₁ = 9610

Thus, the Cost Price (CP) = $9610 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 = 49%

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

= 49% of m

= 49% × m

= ⁴⁹/₁₀₀ × m

⇒ loss = ^{49 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

⇒ 4901.1 = m – ^{49 m}/₁₀₀

⇒ 4901.1 = ^{100 m – 49 m}/₁₀₀

⇒ 4901.1 = ^{51 m}/₁₀₀

After cross multiplication, we get

4901.1 × 100 = 51 m

⇒ 51 m = 4901.1 × 100

⇒ m = ^{4901.1 × 100}/₅₁

⇒ m = ^{4901.1 × 100}/₅₁

⇒ m = ⁴⁹⁰¹¹⁰/₅₁ = 9610

Thus, the Cost Price (CP) = $9610 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) = $4901.1

And, the loss = 49%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 49% of 100 = 49

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

⇒ Sale Price (SP) = 100 – 49

⇒ Sale Price (SP) = 51

∵ If the Sale Price (SP) is 51, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₅₁

∴ If the Sale Price (SP) is 4901.1, then the Cost Price (CP)

= ¹⁰⁰/₅₁ × 4901.1

= ^{100 × 4901.1}/₅₁ = 9610

Thus, the Cost Price (CP) = $9610 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) = $4901.1

And, the loss = 49%

Then, the Cost Price (CP) = ?

SP = 51% of CP

⇒ SP = 51% of CP

⇒ 4901.1 = ⁵¹/₁₀₀ × CP

⇒ 4901.1 = ^{51 CP}/₁₀₀

After cross multiplication

⇒ 4901.1 × 100 = 51 CP

⇒ 51 CP = 4901.1 × 100

⇒ CP = ^{4901.1 × 100}/₅₁

⇒ CP = ⁴⁹⁰¹¹⁰/₅₁ = 9610

⇒ CP = $9610 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 = 49%

And the Sale Price = $4901.1

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

⇒ 100 – 49% of the Cost Price = $4901.1

⇒ 51% of the Cost Price = 4901.1

Therefore, 1% of the Cost Price = ^4901.1/₅₁

Thus, 100% the Cost Price = ^4901.1/₅₁ × 100

= ⁴⁹⁰¹¹⁰/₅₁ = 9610

Thus the Cost Price (CP) = $9610 Answer

Similar Questions

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

(3) William loses 69% by selling an article for $1026.10. For how much should he sell it to get a profit of 68%?

(4) Mr. Oliver loses 83% by selling an article for $681.70. For how much should he sell it to get a profit of 82%?

(5) If a hawker bought 23 apples per $1 and sold them at a rate of 22 apples per $1, then what would his profit percent be?

(6) Mrs. Mary loses 19% by selling an article for $656.10. For how much should she sell it to get a profit of 18%?

(7) Find the cost price, if Mr. Jojo earns a profit of 355% by selling some articles for $31895.5

(8) If a hawker bought 63 candies for $1 and sold them at a rate of 62 candies per $1 then, find the profit percent.

(9) Mrs. Julie buys 16 oranges for $1 and sells 15 oranges for $1. What is her profit percent in this sale?

(10) Bill sold his bicycle at a profit of 15%. If he purchased that bicycle at $200 then find the sale price of the cycle.