varun289 wrote:A kilogram of nut mixture contains X% chestnuts and Y% walnuts and sells for $7.00/kg. If the ratio of chestnuts is increased by 50% so that the new mixture is sold for $8.00/kg, what is the price of a kg of walnuts?
Let us assume, price of a kg of chestnut is C and that of walnuts is W.
Initial ratio of chestnuts and walnuts = X/Y = n
Let us assume that we have mixed n kg of chestnuts and (1 - n) kg of walnuts to get a total of 1 kg mixture.
So, total price = nC + (1 - n)W = 7 ........................ (A)
New ratio = x/y + 50% 0f x/y = 3x/2y = 3n/2 = 1.5n
Let us assume, we have mixed 1.5n kg of chestnuts and (1 - 1.5n) kg of walnuts to get a total of 1 kg mixture.
So, total price = 1.5nC + (1 - 1.5n)W = 8 ---> 3nC + (2 - 3n)W = 16 ........................ (B)
Multiplying (A) with 3 and subtracting (B) from it, 3*(1 - n)W - (2 - 3n)W = 21 - 16
--> 3W - 3nW - 2W + 3nW = 5
--> W = 5
The correct answer is C.
