a man buys an item from delhi 10% cheaper than that at merath, incurs loss of rs. 160, but on selling the item profits rs.240. calculate the profit percentage.
To calculate the profit percentage, we need to determine the cost price (CP) and selling price (SP) of the item.
Let's assume the selling price of the item at Merath is SPm.
Since the man buys the item from Delhi at a 10% cheaper price, the cost price at Delhi (CPd) will be 90% of SPm:
CPd = 0.90 * SPm
We know that the man incurs a loss of Rs. 160, which means the selling price in Delhi (SPd) is equal to the cost price in Delhi (CPd) minus the loss:
SPd = CPd - Loss
SPd = CPd - Rs. 160
Given that the selling price for the man is Rs. 240 more than the cost price in Delhi, we can write:
SPd = CPd + Profit
SPd = CPd + Rs. 240
Equating the two equations for SPd, we can calculate the cost price in Delhi (CPd):
CPd - Rs. 160 = CPd + Rs. 240
Simplifying the equation, we get:
Rs. 240 + Rs. 160 = 2CPd
Rs. 400 = 2CPd
Dividing both sides of the equation by 2, we find:
CPd = Rs. 200
Now, to calculate the selling price in Delhi, we substitute the value of CPd in the equation:
SPd = CPd + Rs. 240
SPd = Rs. 200 + Rs. 240
SPd = Rs. 440
Finally, we can calculate the profit percentage using the formula:
Profit Percentage = (Profit / CP) * 100
Since the profit is Rs. 240 and the cost price is Rs. 200, we substitute these values:
Profit Percentage = (240 / 200) * 100
Profit Percentage = 120%
Therefore, the profit percentage is 120%.
To calculate the profit percentage, we first need to find the cost price (CP) of the item.
Let's assume the cost price at Merath is C, then the cost price of the item in Delhi would be 90% of C since it is 10% cheaper.
So, the cost price in Delhi = 0.90 * C or 0.9C.
Now, let's calculate the selling price (SP):
Profit = SP - CP
Given that the man incurs a loss of Rs. 160, the profit is negative 160. So,
-160 = SP - 0.9C
Rearranging the equation, we have:
SP = 0.9C -160
The selling price is also given as Rs. 240, so:
240 = 0.9C - 160
Adding 160 to both sides of the equation, we get:
400 = 0.9C
Now, dividing both sides of the equation by 0.9, we find:
C = 400 / 0.9
C ≈ 444.44
So, the cost price of the item at Merath is approximately Rs. 444.44.
Now let's calculate the profit percentage:
Profit percentage = (Profit / CP) * 100
Profit = SP - CP = 240 - 444.44 = -204.44 (since it is a loss)
Profit percentage = (-204.44 / 444.44) * 100 ≈ -46.08
Therefore, the profit percentage is approximately -46.08%.