The price of a pair of trousers was decreased by 22% to $30. What was the original price of the trousers?
We will assume that the original price before price reduction = x
The price was decreased by 22%
Then the price after sale = The original [price - the amount reduced
= x - (22% x) = 30
But given that the vurrent price ( after reductions) = $ 30
Then we will write:
x - 22%*x = 30
But 22% = 22/100 = 0.22
==> x - 0.22 x = 30
==> 0.78 x = 30
Now we will divide by 0.78
==> x = 30/ 0.78 = 38.46 ( approx.)
Then the original price of the trousers was = $ 38.46
Here the 30 dollar is the result after decreasing the 22% discount from the original price.
So if the original price is 100%, after decreasing the 22% , the resulting price should be (100-22)% = 78% of the original price.
So the question is if 88%of the original price is $30, then what should be the original price.
We can now easily see that $30 should be multiplied by 100/78.
So the original price should be 30*100/88 = $38.76