Question:
Find the cost price, if Mrs. Mary earns a profit of 270% by selling some articles for $19647
Correct Answer
5310
Solution And Explanation
Solution
Finding the cost price if the sale price and profit percent are known
The cost price (CP) can be found using the formula, algebraic method, using shortcut method, and taking the cost price as 100, 200, 300, 400, 500, or whatever you want.
Finding the cost price using the formula when the sale price and profit percent are known
Given, the sale price (SP) = $19647
And, the profit = 270%
Then, the Cost Price (CP) = ?
Formula to find the cost price when the sale price and profit percent are known
Cost Price (CP) = 100/100 + gain% × SP
Thus, the Cost Price (CP)
= 100/100 + 270 × 19647
= 100 × 19647/370
= 1964700/370 = 5310
Thus, the Cost Price (CP) = $5310 Answer
Finding the cost price (CP) using the Algebraic Method when the Sale Pric (SP) and the profit percent are given
Let the Cost Price (CP) = m
Here given profit = 270%
Calculation of Profit
Profit is calculated on cost price (CP)
Formula to find the Profit = Profit% of CP
Thus, profit on the cost price of m
= 270% of m
= 270% × m
= 270/100 × m
⇒ Profit = 270 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) + Profit
⇒ 19647 = m + 270 m/100
⇒ 19647 = 100 m + 270 m/100
⇒ 19647 = 370 m/100
After cross multiplication, we get
19647 × 100 = 370 m
⇒ 370 m = 19647 × 100
⇒ m = 19647 × 100/370
⇒ m = 1964700/370 = 5310
⇒ m = 5310
Thus, the Cost Price (CP) = $5310 Answer
Finding the cost price (CP) using Unitary Method by taking the cost price (CP) is equal to 100 when the SP and the profit percent are given
Given, the sale price (SP) = $19647
And, the profit = 270%
Then, the Cost Price (CP) = ?
Let Cost Price (CP) = 100
Thus profit = 270% of 100 = 270
Thus, Sale Price (SP) = Cost Price (CP) + Profit
⇒ Sale Price (SP) = 100 + 270
⇒ Sale Price (SP) = 370
∵ If the Sale Price (SP) is 370, then the Cost Price (CP) = 100
∴ If the Sale Price (SP) is 1, then the Cost Price (CP)
= 100/370
∴ If the Sale Price (SP) is 19647, then the Cost Price (CP)
= 100/370 × 19647
= 100 × 19647/370
= 1964700/370 = 5310
Thus, the Cost Price (CP) = $5310 Answer
Shortcut Method to find Cost Price (CP) when SP and profit percent are known
Given, the sale price (SP) = $19647
And, the profit = 270%
Then, the Cost Price (CP) = ?
SP = 370% of CP
⇒ SP = 370/100 × CP
⇒ 19647 = 370 CP/100
After cross multiplication
⇒ 19647 × 100 = 370 CP
⇒ 370 CP = 19647 × 100
⇒ CP = 19647 × 100/370
⇒ CP = 1964700/370 = 5310
⇒ CP = $5310 Answer
Similar Questions
(1) If a trader gets a loss of 25% by selling some shares for $3607.50, then find the cost price of those shares.
(2) Find the cost price, if a shopkeeper earns a profit of 240% by selling an article for $16014
(3) Mr. John earns a profit of 190% by selling a old car for $10759. For how much had he purchased that house?
(4) What will be profit percent if a peddler buys 12 kiwis for $1 and sells 11 kiwis for $1?
(5) If a vendor bought 20 apples per $1 and sold them at a rate of 19 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) William loses 74% by selling an article for $925.60. For how much should he sell it to get a profit of 73%?
(8) A street seller buys 8 articles for $1 and sells 7 articles for $1. Find the profit percent in this sale.
(9) A trader earns a profit of 100% by selling an article for $3820.00. Find the cost price.
(10) A trader earns a profit of 95% by selling an article for $3529.50. What was his cost price?