Question:
If a vendor gets a loss of 21% by selling some apples for $3167.90 then what was the cost price of those apples?
Correct Answer
$4010
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) = $3167.9
And, the loss = 21%
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 – 21 × 3167.9
= 100/79 × 3167.9
= 316790/79 = 4010
Thus, the Cost Price (CP) = $4010 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 = 21%
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
= 21% of m
= 21% × m
= 2/100 × m
⇒ loss = 21 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
⇒ 3167.9 = m – 21 m/100
⇒ 3167.9 = 100 m – 21 m/100
⇒ 3167.9 = 79 m/100
After cross multiplication, we get
3167.9 × 100 = 79 m
⇒ 79 m = 3167.9 × 100
⇒ m = 3167.9 × 100/79
⇒ m = 3167.9 × 100/79
⇒ m = 316790/79 = 4010
Thus, the Cost Price (CP) = $4010 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) = $3167.9
And, the loss = 21%
Then, the Cost Price (CP) = ?
Let Cost Price (CP) = 100
Thus loss = 21% of 100 = 21
Thus, Sale Price (SP) = Cost Price (CP) – loss
⇒ Sale Price (SP) = 100 – 21
⇒ Sale Price (SP) = 79
∵ If the Sale Price (SP) is 79, then the Cost Price (CP) = 100
∴ If the Sale Price (SP) is 1, then the Cost Price (CP)
= 100/79
∴ If the Sale Price (SP) is 3167.9, then the Cost Price (CP)
= 100/79 × 3167.9
= 100 × 3167.9/79 = 4010
Thus, the Cost Price (CP) = $4010 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) = $3167.9
And, the loss = 21%
Then, the Cost Price (CP) = ?
SP = 79% of CP
⇒ SP = 79% of CP
⇒ 3167.9 = 79/100 × CP
⇒ 3167.9 = 79 CP/100
After cross multiplication
⇒ 3167.9 × 100 = 79 CP
⇒ 79 CP = 3167.9 × 100
⇒ CP = 3167.9 × 100/79
⇒ CP = 316790/79 = 4010
⇒ CP = $4010 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 = 21%
And the Sale Price = $3167.9
This means 100 – loss% of the Cost Price = Sale Price
⇒ 100 – 21% of the Cost Price = $3167.9
⇒ 79% of the Cost Price = 3167.9
Therefore, 1% of the Cost Price = 3167.9/79
Thus, 100% the Cost Price = 3167.9/79 × 100
= 316790/79 = 4010
Thus the Cost Price (CP) = $4010 Answer
Similar Questions
(1) A dealer sold an antique piece of a car $25771.50. If he earns a profit of 315%, then find his cost price.
(2) Find the cost price, if a dealer gets a loss of 30% by selling 300 stocks for $4067
(3) If a trader gets a loss of 13% by selling some colthes for $2096.70 then find the cost price.
(4) A dealer loses 21% by selling an article for $718.90. For how much should he sell it to get a profit of 20%?
(5) If a vendor bought 62 candies for $1 and sold 61 candies per $1 then find the profit percent.
(6) If a trader earns a profit of 45% by selling an article for $1174.5, then find the cost price.
(7) A peddler purchased 25 apples per $1 and sold them at a rate of 24 apples per $1. What will be the profit percent?
(8) Find the cost price, if a trader gets a loss of 40% by selling 1000 packets of fruits for $4686
(9) If a trader earned a profit of 350% by selling a housing plot for $31095 then, what was the cost price of the plot?
(10) What is the cost price, if Mrs. Jill earns a profit of 200% by selling some items for $11730?