Question:
Find the cost price, if a trader earns a profit of 5% by selling an article for $10.5
Correct Answer
10
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) = $10.5
And, the profit = 5%
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 + 5 × 10.5
= 100 × 10.5/105
= 1050/105 = 10
Thus, the Cost Price (CP) = $10 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 = 5%
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
= 5% of m
= 5% × m
= 5/100 × m
⇒ Profit = 5 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) + Profit
⇒ 10.5 = m + 5 m/100
⇒ 10.5 = 100 m + 5 m/100
⇒ 10.5 = 105 m/100
After cross multiplication, we get
10.5 × 100 = 105 m
⇒ 105 m = 10.5 × 100
⇒ m = 10.5 × 100/105
⇒ m = 1050/105 = 10
⇒ m = 10
Thus, the Cost Price (CP) = $10 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) = $10.5
And, the profit = 5%
Then, the Cost Price (CP) = ?
Let Cost Price (CP) = 100
Thus profit = 5% of 100 = 5
Thus, Sale Price (SP) = Cost Price (CP) + Profit
⇒ Sale Price (SP) = 100 + 5
⇒ Sale Price (SP) = 105
∵ If the Sale Price (SP) is 105, then the Cost Price (CP) = 100
∴ If the Sale Price (SP) is 1, then the Cost Price (CP)
= 100/105
∴ If the Sale Price (SP) is 10.5, then the Cost Price (CP)
= 100/105 × 10.5
= 100 × 10.5/105
= 1050/105 = 10
Thus, the Cost Price (CP) = $10 Answer
Shortcut Method to find Cost Price (CP) when SP and profit percent are known
Given, the sale price (SP) = $10.5
And, the profit = 5%
Then, the Cost Price (CP) = ?
SP = 105% of CP
⇒ SP = 105/100 × CP
⇒ 10.5 = 105 CP/100
After cross multiplication
⇒ 10.5 × 100 = 105 CP
⇒ 105 CP = 10.5 × 100
⇒ CP = 10.5 × 100/105
⇒ CP = 1050/105 = 10
⇒ CP = $10 Answer
Similar Questions
(1) After selling some items for $6884.50 Mr. Bob earns 145%. Find the cost price of those items.
(2) Jojo loses 36% by selling an article for $1062.40. For how much should he sell it to get a profit of 35%?
(3) If a broker gets a loss of 23% by selling 200 shares he had for $3395.70 then find the cost price of those shares.
(4) A shopkeeper loses 22% by selling an article for $748.80. For how much should he sell it to get a profit of 21%?
(5) A dealer loses 57% by selling an article for $1165.30. For how much should he sell it to get a profit of 56%?
(6) Find the cost price, if a trader gets a loss of 61% by selling 4 TV sets for $4683.90
(7) If a shopkeeper loses 6% by selling some items for $150.40 then, for how much should he sell them to get a profit of 5%?
(8) In an exhibition, a trader earns a profit of 75%. His total sale was $2467.50. Find the cost price.
(9) John loses 62% by selling an article for $1124.80. For how much should he sell it to get a profit of 61%?
(10) After selling some antique items for $6504 a trader earns a profit of 140%. Find the cost price of those antique items.