Question:
On a closing day, a shopkeeper earns a profit of 65%. If gets $1996.5 in total, then what was his cost price?
Correct Answer
1210
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) = $1996.5
And, the profit = 65%
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 + 65 × 1996.5
= 100 × 1996.5/165
= 199650/165 = 1210
Thus, the Cost Price (CP) = $1210 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 = 65%
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
= 65% of m
= 65% × m
= 65/100 × m
⇒ Profit = 65 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) + Profit
⇒ 1996.5 = m + 65 m/100
⇒ 1996.5 = 100 m + 65 m/100
⇒ 1996.5 = 165 m/100
After cross multiplication, we get
1996.5 × 100 = 165 m
⇒ 165 m = 1996.5 × 100
⇒ m = 1996.5 × 100/165
⇒ m = 199650/165 = 1210
⇒ m = 1210
Thus, the Cost Price (CP) = $1210 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) = $1996.5
And, the profit = 65%
Then, the Cost Price (CP) = ?
Let Cost Price (CP) = 100
Thus profit = 65% of 100 = 65
Thus, Sale Price (SP) = Cost Price (CP) + Profit
⇒ Sale Price (SP) = 100 + 65
⇒ Sale Price (SP) = 165
∵ If the Sale Price (SP) is 165, then the Cost Price (CP) = 100
∴ If the Sale Price (SP) is 1, then the Cost Price (CP)
= 100/165
∴ If the Sale Price (SP) is 1996.5, then the Cost Price (CP)
= 100/165 × 1996.5
= 100 × 1996.5/165
= 199650/165 = 1210
Thus, the Cost Price (CP) = $1210 Answer
Shortcut Method to find Cost Price (CP) when SP and profit percent are known
Given, the sale price (SP) = $1996.5
And, the profit = 65%
Then, the Cost Price (CP) = ?
SP = 165% of CP
⇒ SP = 165/100 × CP
⇒ 1996.5 = 165 CP/100
After cross multiplication
⇒ 1996.5 × 100 = 165 CP
⇒ 165 CP = 1996.5 × 100
⇒ CP = 1996.5 × 100/165
⇒ CP = 199650/165 = 1210
⇒ CP = $1210 Answer
Similar Questions
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(2) For how much should he sell it to get a profit of 16%, if Mr. Bond loses 17% by selling a bicycle for $589.30?
(3) William loses 33% by selling an article for $1011.70. For how much should he sell it to get a profit of 32%?
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(5) By selling a house for $14332.50, a dealer earns a profit of 225%. Find the cost price
(6) 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?
(7) Peter buys 5 articles for $1 and sells 4 articles for $1. Find the profit percent in this sale.
(8) Mr. Donald loses 85% by selling an article for $616.50. For how much should he sell it to get a profit of 84%?
(9) How much percent will a vendor earn, if he buys 35 articles for $1 and sells 34 articles for $1?
(10) If a vendor gets a loss of 21% by selling some apples for $3167.90 then what was the cost price of those apples?