I actually worked backwards using the answer choices instead of using an equation.
At $3, you can buy 40 towels right?
Now if the price is increased to $4, you can buy 30 towels now for $120.
A store currently charges the same price for each towe that it sells. If the current price of each towel were to be increased by $1, 10 fewer of the towels could be bought for $120, excluding sales tax. What is the current price of each towel?
(A) $1
(B) $2
(C) $3
(D) $4
(E) $12
I don't understand the phrase "10 fewer of the towels could be bought for $120" so this one completely threw me off. (Taken from PowerPrep CAT 2)
Yes Ritesh's method is the shortcut.
The long method is ..
let number of towels bought for $120 = n
so price of a single towel = $ 120 / n
now price of 1 towel increases by $ 1
so new price of a single towel = $ (120 / n) + 1
no. of towel that could be bought at this price = n - 10
so new price of a single towel = $ 120 / (n -10)
so equating
so (120/n) + 1 = 120 / (n - 10)
(120 + n) / n = 120 / (n - 10)
n^2 -10n - 1200 = 0
(n-40)(n+30) = 0
n = 40 or n = -30
n= 40 = number of towels that could be bought at current price.
=> current price per towel = $ 120 / 40 = $ 3
so ans is C
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