When a shirt is sold at sh 126 a Ioss of x%is made if the same shirt is sold at sh154 a profit ofx% is realized find the buying price
Let's assume the buying price of the shirt is y.
When the shirt is sold at sh 126, a loss of x% is made. This means that the selling price is (100 - x)% of the buying price. Therefore, the selling price is 0.01(100 - x)y = 0.01(100y - xy) = y - 0.01xy.
When the shirt is sold at sh 154, a profit of x% is made. This means that the selling price is (100 + x)% of the buying price. Therefore, the selling price is 0.01(100 + x)y = 0.01(100y + xy) = y + 0.01xy.
We can now set up the equation:
y - 0.01xy = 126
y + 0.01xy = 154
By simplifying the equations, we get:
y - 0.01xy = 126
y + 0.01xy = 154
Adding the two equations together eliminates the term with xy:
2y = 280
Dividing both sides by 2:
y = 140
Therefore, the buying price of the shirt is sh 140.
To find the buying price of the shirt, we can use the formula for calculating profit or loss percentage:
Profit or Loss percentage = (Selling Price - Cost Price) / Cost Price * 100
Let's assume the cost price of the shirt is CP.
For the first scenario where the shirt is sold at sh126 with a loss of x%, we can write the equation as:
x% = (sh126 - CP) / CP * 100
Now, let's rearrange the equation to solve for CP:
x% / 100 = (sh126 - CP) / CP
Moving the denominator to the left-hand side:
CP * (x% / 100) = sh126 - CP
Expanding:
CP * x% / 100 = sh126 - CP
Multiplying both sides by 100:
CP * x% = 100(sh126 - CP)
Simplifying:
CP * x% = 100sh126 - 100CP
Bringing the terms with CP to one side:
CP * x% + 100CP = 100sh126
Factoring out CP:
CP(x% + 100) = 100sh126
Dividing both sides by (x% + 100):
CP = (100sh126) / (x% + 100)
Now, let's calculate the buying price for the second scenario where the shirt is sold at sh154 with a profit of x%:
Using the same formula as before:
x% = (sh154 - CP) / CP * 100
Rearranging the equation to solve for CP:
CP * (x% / 100) = sh154 - CP
Expanding:
CP * x% / 100 = sh154 - CP
Simplifying:
CP * x% = 100(sh154 - CP)
Bringing the terms with CP to one side:
CP * x% + 100CP = 100sh154
Factoring out CP:
CP(x% + 100) = 100sh154
Dividing both sides by (x% + 100):
CP = (100sh154) / (x% + 100)
Therefore, the buying price of the shirt is given by:
CP = (100sh126) / (x% + 100) = (100sh154) / (x% + 100)