A rice merchant has four verieties of rice - A,B,C,D with him. He mixed the entire quantity of rice of verieties A and B. With this mixture, if he mixes the entire quantity of rice of variety C, which cost Rs 20/kg, mixture so formed would cost 25/kg. Instead if he mixes with it the entire quantity of rice of veriety D, which costs Rs 36/kg, the mixture so formed would cost Rs 31 per kg, if the entire quantity of veriety D is thrice that of rice of veriety C, how much would the mixture of the entire quantity of rice of all 4 veriety cost.

Solution(By Examveda Team)

ANSWER = 29.5 Rs/kg

SOLUTION:
Let us consider the mixture of variety A and B as a single entity say variety P.
Let total quantity of P be y kg and its cost be a Rs/kg.
Let total quantity of C be x kg and its cost is 20 Rs/kg.
Let total quantity of D be 3x kg and its cost is 36 Rs/kg.
First case, mixing variety P with variety C,
∴ y*a +20x = 25 * (x+y)
∴ y*a = 25y +5x -------(1)

Second case mixing variety P with variety D,
∴ y*a + (3x) * 36 = 31 * (y+3x)
∴ y*a = 31y-15x -------(2)

Comparing (1) and (2),
25y + 5x = 31y - 15x
10x = 3y
x/y = 3/10 -------(3)

Finally mixing all the varieties P(A and B), C and D.
Total Cost = y*a + 20x + 36 * (3x) = y*a + 128x = (25y +5x) + 128x =25y + 133x {USING EQUATION (1)}
Total quantity = y + x + 3x = (y + 4x) kg
∴ Cost per kg = (25y + 133x) / (y + 4x) = (250 + 399) / (10 + 12) {USING EQUATION (3)}
∴ Cost per kg = 649/22 = 29.5 Rs/kg