Question:
Find the cost price, if a trader gets a loss of 19% by selling an article for $2924.10
Correct Answer
$3610
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) = $2924.1
And, the loss = 19%
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 – 19 × 2924.1
= 100/81 × 2924.1
= 292410/81 = 3610
Thus, the Cost Price (CP) = $3610 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 = 19%
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
= 19% of m
= 19% × m
= 2/100 × m
⇒ loss = 19 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
⇒ 2924.1 = m – 19 m/100
⇒ 2924.1 = 100 m – 19 m/100
⇒ 2924.1 = 81 m/100
After cross multiplication, we get
2924.1 × 100 = 81 m
⇒ 81 m = 2924.1 × 100
⇒ m = 2924.1 × 100/81
⇒ m = 2924.1 × 100/81
⇒ m = 292410/81 = 3610
Thus, the Cost Price (CP) = $3610 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) = $2924.1
And, the loss = 19%
Then, the Cost Price (CP) = ?
Let Cost Price (CP) = 100
Thus loss = 19% of 100 = 19
Thus, Sale Price (SP) = Cost Price (CP) – loss
⇒ Sale Price (SP) = 100 – 19
⇒ Sale Price (SP) = 81
∵ If the Sale Price (SP) is 81, then the Cost Price (CP) = 100
∴ If the Sale Price (SP) is 1, then the Cost Price (CP)
= 100/81
∴ If the Sale Price (SP) is 2924.1, then the Cost Price (CP)
= 100/81 × 2924.1
= 100 × 2924.1/81 = 3610
Thus, the Cost Price (CP) = $3610 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) = $2924.1
And, the loss = 19%
Then, the Cost Price (CP) = ?
SP = 81% of CP
⇒ SP = 81% of CP
⇒ 2924.1 = 81/100 × CP
⇒ 2924.1 = 81 CP/100
After cross multiplication
⇒ 2924.1 × 100 = 81 CP
⇒ 81 CP = 2924.1 × 100
⇒ CP = 2924.1 × 100/81
⇒ CP = 292410/81 = 3610
⇒ CP = $3610 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 = 19%
And the Sale Price = $2924.1
This means 100 – loss% of the Cost Price = Sale Price
⇒ 100 – 19% of the Cost Price = $2924.1
⇒ 81% of the Cost Price = 2924.1
Therefore, 1% of the Cost Price = 2924.1/81
Thus, 100% the Cost Price = 2924.1/81 × 100
= 292410/81 = 3610
Thus the Cost Price (CP) = $3610 Answer
Similar Questions
(1) If a dealer gets a loss of 75% by selling 200 boxes of apple for $3702.50 then find the cost price.
(2) To get a profit of 15% Mr. John should sell his old bicycle for how much, if he loses 16% by selling it for $554.40?
(3) If a shopkeeper gets a loss of 53% by selling 200 kg of rice for $4892.70 then find the cost price of rice.
(4) Mrs. Mary earns a profit of 230% after selling an article for $14883. Find the cost price.
(5) If a vendor bought 21 apples per $1 and sold them at a rate of 20 apples per $1, then what would his profit percent be?
(6) For how much should a trader sell an item to get a profit of 49% if he loses 50% by selling it for $1180.00?
(7) Mr. Oliver loses 81% by selling an article for $742.90. For how much should he sell it to get a profit of 80%?
(8) How much Mr. Gates had to pay to purchase his motorbike? If he gets a profit of 70% after selling it for $2227.
(9) Find the cost price, if a trader gets a loss of 36% by selling 500 packets of fruits for $4486.40
(10) What is the cost price if a trader earns a profit of 155% by selling an article for $7675.50