Sriharsh wrote:

A shopkeeper mixes three varieties of rice costing $10, $12, $17 per kg. Which of the following can represent a possible ratio in which the three varieties are mixed, if the trader makes a profit of 20% by selling the mixture at $15.60 per kg?

(A) 9:14:36

(B) 11:14:25

(C) 14:36:43

(D) 2:6:3

(E) None of these

OA:DLet the weight of each variety in the mixture be \(x,y,\) and \(z\) kg

Weight of the total mixture \(=x+y+z\)

Cost price + Profit = Selling price

Cost price \(= 10x+12y+17z\)

Profit \(=\frac{20}{100}\) Cost price \(= 0.2\) Cost price

Selling price \(= 15.6(x+y+z)\)

\(10x+12y+17z +0.2(10x+12y+17z)= 15.6(x+y+z)\)

\(1.2(10x+12y+17z)=15.6(x+y+z)\)

\(10x+12y+17z = 13(x+y+z)\)

\(3x+y-4z=0\)

Only Option D satisfies \(3x+y-4z=0\)

As per option D, \(x=2m,y=6m\) and \(z=3m\)

L.H.S : \(3x+y-4z = 3*2m+6m-4*3m = 6m+6m-12m=0\)

R.H.S : \(0\)

\(L.H.S=R.H.S\)