To find the cost price (C.P.) of an object when you have the selling price (S.P.) and the profit percentage, you can use the following relationship:
Profit = Selling Price - Cost Price (Profit = S.P. - C.P.)
The profit percentage is given by:
Profit Percentage = (Profit / Cost Price) 100
Since we have the profit percentage and the selling price, we can manipulate these equations to find the cost price.
First, let's set up the formula using the profit percentage:
Profit = (Profit Percentage / 100) Cost Price
We will rearrange the terms to isolate the cost price:
Cost Price = Profit / (Profit Percentage / 100)
But we don't have the profit directly; we only have the selling price and the profit percentage. So we need to express the profit in terms of the selling price and the profit percentage.
Since Profit + Cost Price = Selling Price, we can rewrite this as
Profit = Selling Price - Cost Price
Now, substituting the expression for profit in terms of profit percentage and cost price, we have:
Profit = (Profit Percentage / 100) Cost Price
So, Selling Price - Cost Price = (Profit Percentage / 100) Cost Price
Adding Cost Price to both sides to get terms involving Cost Price on one side, we get:
Selling Price = Cost Price + (Profit Percentage / 100) Cost Price
Now we can factor out the Cost Price:
Selling Price = Cost Price (1 + (Profit Percentage / 100))
And finally, we isolate the Cost Price:
Cost Price = Selling Price / (1 + (Profit Percentage / 100))
Now let's substitute the given values:
Selling Price (S.P.) = Rs. 332.8
Profit Percentage (Profit%) = 30%
Cost Price = Selling Price / (1 + (Profit Percentage / 100))
Cost Price = Rs. 332.8 / (1 + (30 / 100))
Cost Price = Rs. 332.8 / (1 + 0.3)
Cost Price = Rs. 332.8 / 1.3
Doing the division:
Cost Price = Rs. 256
Therefore, the correct answer is:
d. Rs. 256
