Question:
Find the cost price, if a trader gets a loss of 74% by selling 50 bags of rice for $3798.60
Correct Answer
$14610
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) = $3798.6
And, the loss = 74%
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 – 74 × 3798.6
= 100/26 × 3798.6
= 379860/26 = 14610
Thus, the Cost Price (CP) = $14610 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 = 74%
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
= 74% of m
= 74% × m
= 74/100 × m
⇒ loss = 74 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
⇒ 3798.6 = m – 74 m/100
⇒ 3798.6 = 100 m – 74 m/100
⇒ 3798.6 = 26 m/100
After cross multiplication, we get
3798.6 × 100 = 26 m
⇒ 26 m = 3798.6 × 100
⇒ m = 3798.6 × 100/26
⇒ m = 3798.6 × 100/26
⇒ m = 379860/26 = 14610
Thus, the Cost Price (CP) = $14610 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) = $3798.6
And, the loss = 74%
Then, the Cost Price (CP) = ?
Let Cost Price (CP) = 100
Thus loss = 74% of 100 = 74
Thus, Sale Price (SP) = Cost Price (CP) – loss
⇒ Sale Price (SP) = 100 – 74
⇒ Sale Price (SP) = 26
∵ If the Sale Price (SP) is 26, then the Cost Price (CP) = 100
∴ If the Sale Price (SP) is 1, then the Cost Price (CP)
= 100/26
∴ If the Sale Price (SP) is 3798.6, then the Cost Price (CP)
= 100/26 × 3798.6
= 100 × 3798.6/26 = 14610
Thus, the Cost Price (CP) = $14610 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) = $3798.6
And, the loss = 74%
Then, the Cost Price (CP) = ?
SP = 26% of CP
⇒ SP = 26% of CP
⇒ 3798.6 = 26/100 × CP
⇒ 3798.6 = 26 CP/100
After cross multiplication
⇒ 3798.6 × 100 = 26 CP
⇒ 26 CP = 3798.6 × 100
⇒ CP = 3798.6 × 100/26
⇒ CP = 379860/26 = 14610
⇒ CP = $14610 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 = 74%
And the Sale Price = $3798.6
This means 100 – loss% of the Cost Price = Sale Price
⇒ 100 – 74% of the Cost Price = $3798.6
⇒ 26% of the Cost Price = 3798.6
Therefore, 1% of the Cost Price = 3798.6/26
Thus, 100% the Cost Price = 3798.6/26 × 100
= 379860/26 = 14610
Thus the Cost Price (CP) = $14610 Answer
Similar Questions
(1) A trader earns a profit of 205% by selling some articles for $12230.50. What was the cost price?
(2) If Mr. Peter buys 17 apples for $1 and sells 16 apples for $1 then, find the profit percent in this sale.
(3) A dealer loses 60% by selling an article for $1144.00. For how much should he sell it to get a profit of 59%?
(4) If a book seller gets a loss of 33% by selling 300 books for $4294.70 then find the cost price of the books.
(5) Oliver loses 35% by selling an article for $1046.50. For how much should he sell it to get a profit of 34%?
(6) Find the profit percent if a vendor buys 9 articles for $1 and sells 8 articles for $1.
(7) Find the cost price, if a trader gets a loss of 47% by selling 500 kg rice for $4881.30
(8) Mr. Donald loses 84% by selling an article for $649.60. For how much should he sell it to get a profit of 83%?
(9) Find the cost price, if a shopkeeper earns a profit of 240% by selling an article for $16014
(10) For how much should Mr. Bose sell his furniture to get a profit of 28%, if he loses 29% by selling it for $930.10?