Question:
If a trader gets a loss of 20% by selling some apples for $3048, then find the cost price of those apples.
Correct Answer
$3810
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) = $3048
And, the loss = 20%
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 – 20 × 3048
= 100/80 × 3048
= 304800/80 = 3810
Thus, the Cost Price (CP) = $3810 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 = 20%
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
= 20% of m
= 20% × m
= 2/100 × m
⇒ loss = 20 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
⇒ 3048 = m – 20 m/100
⇒ 3048 = 100 m – 20 m/100
⇒ 3048 = 80 m/100
After cross multiplication, we get
3048 × 100 = 80 m
⇒ 80 m = 3048 × 100
⇒ m = 3048 × 100/80
⇒ m = 3048 × 100/80
⇒ m = 304800/80 = 3810
Thus, the Cost Price (CP) = $3810 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) = $3048
And, the loss = 20%
Then, the Cost Price (CP) = ?
Let Cost Price (CP) = 100
Thus loss = 20% of 100 = 20
Thus, Sale Price (SP) = Cost Price (CP) – loss
⇒ Sale Price (SP) = 100 – 20
⇒ Sale Price (SP) = 80
∵ If the Sale Price (SP) is 80, then the Cost Price (CP) = 100
∴ If the Sale Price (SP) is 1, then the Cost Price (CP)
= 100/80
∴ If the Sale Price (SP) is 3048, then the Cost Price (CP)
= 100/80 × 3048
= 100 × 3048/80 = 3810
Thus, the Cost Price (CP) = $3810 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) = $3048
And, the loss = 20%
Then, the Cost Price (CP) = ?
SP = 80% of CP
⇒ SP = 80% of CP
⇒ 3048 = 80/100 × CP
⇒ 3048 = 80 CP/100
After cross multiplication
⇒ 3048 × 100 = 80 CP
⇒ 80 CP = 3048 × 100
⇒ CP = 3048 × 100/80
⇒ CP = 304800/80 = 3810
⇒ CP = $3810 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 = 20%
And the Sale Price = $3048
This means 100 – loss% of the Cost Price = Sale Price
⇒ 100 – 20% of the Cost Price = $3048
⇒ 80% of the Cost Price = 3048
Therefore, 1% of the Cost Price = 3048/80
Thus, 100% the Cost Price = 3048/80 × 100
= 304800/80 = 3810
Thus the Cost Price (CP) = $3810 Answer
Similar Questions
(1) Find the cost price, if a dealer earns a profit of 380% by selling an article for $36048
(2) 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.
(3) Find the cost price, if a trader gets a loss of 64% by selling five TV sets for $4539.6
(4) Mr. Noah loses 37% by selling an article for $1077.30. For how much should he sell it to get a profit of 36%?
(5) A dealer loses 23% by selling an article for $777.7. For how much should he sell it to get a profit of 22%?
(6) Find the cost price, if a vendor gets a loss of 56% by selling a TV set for $4844.40.
(7) Find the cost price, if a dealer earns a profit of 345% by selling some goods for $30304.5
(8) Find the cost price, if a trader earns a profit of 5% by selling an article for $10.5
(9) Find the cost price, if a trader gets a loss of 19% by selling an article for $2924.10
(10) What will the earnings in percent if a vendor buys 42 apples for $1 and sells at a rate of 41 apples per $1?