Question:
If a trader gets a loss of 72% by selling 15 bags of apples for $3978.80 then find the cost price of the apples.
Correct Answer
$14210
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) = $3978.8
And, the loss = 72%
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 – 72 × 3978.8
= 100/28 × 3978.8
= 397880/28 = 14210
Thus, the Cost Price (CP) = $14210 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 = 72%
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
= 72% of m
= 72% × m
= 72/100 × m
⇒ loss = 72 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
⇒ 3978.8 = m – 72 m/100
⇒ 3978.8 = 100 m – 72 m/100
⇒ 3978.8 = 28 m/100
After cross multiplication, we get
3978.8 × 100 = 28 m
⇒ 28 m = 3978.8 × 100
⇒ m = 3978.8 × 100/28
⇒ m = 3978.8 × 100/28
⇒ m = 397880/28 = 14210
Thus, the Cost Price (CP) = $14210 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) = $3978.8
And, the loss = 72%
Then, the Cost Price (CP) = ?
Let Cost Price (CP) = 100
Thus loss = 72% of 100 = 72
Thus, Sale Price (SP) = Cost Price (CP) – loss
⇒ Sale Price (SP) = 100 – 72
⇒ Sale Price (SP) = 28
∵ If the Sale Price (SP) is 28, then the Cost Price (CP) = 100
∴ If the Sale Price (SP) is 1, then the Cost Price (CP)
= 100/28
∴ If the Sale Price (SP) is 3978.8, then the Cost Price (CP)
= 100/28 × 3978.8
= 100 × 3978.8/28 = 14210
Thus, the Cost Price (CP) = $14210 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) = $3978.8
And, the loss = 72%
Then, the Cost Price (CP) = ?
SP = 28% of CP
⇒ SP = 28% of CP
⇒ 3978.8 = 28/100 × CP
⇒ 3978.8 = 28 CP/100
After cross multiplication
⇒ 3978.8 × 100 = 28 CP
⇒ 28 CP = 3978.8 × 100
⇒ CP = 3978.8 × 100/28
⇒ CP = 397880/28 = 14210
⇒ CP = $14210 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 = 72%
And the Sale Price = $3978.8
This means 100 – loss% of the Cost Price = Sale Price
⇒ 100 – 72% of the Cost Price = $3978.8
⇒ 28% of the Cost Price = 3978.8
Therefore, 1% of the Cost Price = 3978.8/28
Thus, 100% the Cost Price = 3978.8/28 × 100
= 397880/28 = 14210
Thus the Cost Price (CP) = $14210 Answer
Similar Questions
(1) William loses 70% by selling an article for $1008.00 For how much should he sell it to get a profit of 69%?
(2) Calculate the earnings in percent if Mr. Peter buys 66 articles for $1 and sells 65 articles for $1.
(3) A trader loses 30% by selling an article for $952. For how much should he sell it to get a profit of 29%?
(4) John loses 64% by selling an article for $1101.60. For how much should he sell it to get a profit of 63%?
(5) Find the cost price, if a trader gets a loss of 44% by selling 500 packets of fruits for $48210.60
(6) Find the cost price, if a dealer gets a loss of 30% by selling 300 stocks for $4067
(7) If a trader gets a loss of 25% by selling some shares for $3607.50, then find the cost price of those shares.
(8) Find the cost price, if a trader gets a loss of 35% by selling some articles for $4426.50
(9) Mr. Steven loses 95% by selling an article for $230.50. For how much should he sell it to get a profit of 94%?
(10) By selling an article for $1125.30 a vendor gets a loss of 7%. Calculate the cost price.