on selling a bag for rs.704, a shopkeeper suffers a loss of 12% at what price should he sell it to gain 7.5%
To find the selling price at a 7.5% gain, we need to calculate the cost price of the bag first.
Let's assume the cost price of the bag is Rs. X.
Given that the shopkeeper suffered a loss of 12%, we can write the equation for the selling price (SP) as:
SP = X - (12/100) * X
Simplifying the above equation, we get:
SP = X - 0.12X
SP = 0.88X
Since the selling price is Rs. 704, we can equate the above equation with 704:
0.88X = 704
Dividing both sides by 0.88:
X = 704 / 0.88
X = 800
So, the cost price of the bag is Rs. 800.
To find the selling price that would result in a 7.5% gain, we can use the following equation:
SP = CP + (7.5/100) * CP
Substituting the value of CP as Rs. 800 into the equation:
SP = 800 + (7.5/100) * 800
SP = 800 + 0.075 * 800
SP = 800 + 60
SP = 860
Therefore, the shopkeeper should sell the bag for Rs. 860 in order to gain 7.5%.
To find the selling price at which the shopkeeper would gain 7.5%, we need to consider the following steps:
Step 1: Calculate the cost price of the bag.
Since the shopkeeper suffered a loss of 12%, the selling price is 88% (100% - 12%) of the cost price:
Selling price = 88% of cost price
Let the cost price be x.
704 = 0.88x (Converting 88% to decimal form)
x = 704 / 0.88
x = 800
Therefore, the cost price of the bag is Rs. 800.
Step 2: Calculate the selling price to gain 7.5% profit.
Now we need to find the selling price that would yield a 7.5% profit. This means the selling price would be 107.5% (100% + 7.5%) of the cost price:
Selling price = 107.5% of cost price
Selling price = 107.5% of Rs. 800
Selling price = (107.5/100) * 800
Calculating the selling price:
Selling price = 1.075 * 800
Selling price = Rs. 860
Therefore, the shopkeeper should sell the bag for Rs. 860 to gain a 7.5% profit.