Profit And Loss
MCQs Math


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 And 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

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

(3) Mr. Bobby earns a profit of 120% by selling a TV set for $5082. What was the cost price of the TV set?

(4) A dealer loses 58% by selling an article for $1159.20. For how much should he sell it to get a profit of 57%?

(5) Find the cost price, if a dealer gets a loss of 32% by selling 500 books for $4222.80.

(6) Find the cost price if Mr. Rocky earns a profit of 105% by selling an article for $4120.50

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

(8) If a shopkeeper loses 38% by selling some articles for $1091.20 then, he should sell them to get a profit of 37% for how much?

(9) By selling an article for $15443.50, Mrs. Linda earns a profit of 235%. What was the cost price?

(10) What was the cost price, if a trader gets a loss of 17% by selling an article for $2664.30?


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