Question : A seller gets a profit of 7% by selling a TV set for $4280. If he would have sold it for $4200, then find his profit percent.
Correct Answer Profit = 5%
Solution & Explanation
Solution
Given,
Sale Price = $4280
Thus, profit = 7%
When sale price (SP) = $4200
The profit % = ?
Calculation of Cost Price using formula when profit percent and Sale Price (SP) is given
To calculate the profit%, first we need to calculate the cost price
Cost Price (CP)
= 100/100 + profit% × Sale Price (SP)
Thus, Cost Price
= 100/100 + 7 × 4280
= 100/107 × 4280 40
= 100 × 40 = 4000
Therefore, Cost Price (CP) = $4000
Calculation of profit% using formula when CP and SP is known
Here, Sale Price (SP) = $4200
And, Cost Price (CP) = $4000
Profit = Sale Price (SP) – Cost Price (CP)
= 4200 – 4000 = 200
Thus, Profit = $200
Calculation of profit% using formula, when cost price (CP) and profit is known
Profit% = Profit × 100/Cost Price
⇒ Profit% = 200 × 100/4000 20
= 100 5/20 = 5
Thus, profit = 5% Answer
Calculation of Cost Price using Unitary Method when profit percent and Sale Price (SP) is given
Calculation of Cost Price (CP) by taking CP = 100
As given in the question
Sale Price = $4280
Thus, profit = 7%
Thus, if Sale Price (SP) = $4200
Therefore, profit % = ?
Let Cost Prive (CP) = 100
Here, profit = 7%
Thus, profit = 7% of 100 = $7
⇒ Profit = $7
Therefore, Sale Price (SP) = Cost Price (CP) + Profit
⇒ SP = 100 + 7 = 107
Now, ∵ When sale price (SP) is $107, then cost price (CP) = 100
∴ When sale price (SP) is $1, then cost price (CP) = 100/107
∴ When sale price (SP) is $4280, then cost price (CP) = 100/107 × 4280 40
= 100 × 40 = 4000
Thus, Cost Price (CP) = $4000
Calculation of profit when SP = $4200 and CP = $4000
Now, Profit = Sale Price (SP) – Cost Price (CP)
⇒ Profit = $4200 – $4000 = $200
⇒ Proft = $200
Calculation of profit% using Unitary Method, when profit and Cost Price (CP) is known
∵ When cost price is $4000, the profit = $200
∴ When cost price is $1, then profit = 200/4000
∴ When cost price is $100, the profit = 200/4000 20 × 100
= 100 5/20 = 5%
Thus, profit = 5% Answer
Althernate method
Calculation of Cost Price using Algebraic Method
Calculation of cost price by taking Cost Price (CP) as a variable "c": Algebraic Method
As given in the question
Sale Price = $4280
Thus, profit = 7%
Thus, if Sale Price (SP) = $4200
Therefore, profit % = ?
Let, cost price = "c"
We know that
Sale Price (SP) = Cost Price (CP) + profit % of Cost Price(CP)
⇒ Sale Price (SP) = c + 7% of c
⇒ 4280 = c + 7/100 × c
⇒ 4280 = c + 7 c/100
⇒ 4280 = 100 c + 7 c/100
⇒ 4280 = 107 c/100
After cross multiplication, we get
107 c = 4280 × 100
⇒ c = 4280 × 100/107
⇒ c = 4280 40 × 100/107
⇒ c = 40 × 100 = $4000
Therefore, cost price = $4000
Calculation of profit when cost price and sale price are known
Now, the sale price = $4200 and cost price = $4000
Profit = Sale price – Cost Price
Therefore, profit = $4200 – $4000
⇒ Profit = $200
Calculation of profit percent when profit and cost price are known
Here, profit = $200, and cost price = $4000
?% of 4000 = 200
?/100 × 4000 = 200
⇒ ? × 4000/100 = 200
After cross multiplication, we get
? × 4000 = 200 × 100
⇒ ? = 200 × 100/4000
⇒ ? = 5 20000/4000
⇒ ? = 5%
Therefore, profit = 5% Answer
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