Three types of tea (namely a, b and c) costs Rs. 95/kg, Rs. 100/kg and Rs. 70/kg respectively. How many Kg. of each should be blended to produce 100 kg of mixture worth Rs. 90/kg, given that the quantities of band c are equal ?

  1. 70,15,15

  2. 50,25,25

  3. 60,20,20

  4. 40,30,30


Correct Option: B

AI Explanation

To solve this problem, we can use a system of equations.

Let's assume that the quantities of tea a, b, and c in kg are x, y, and z respectively.

Given: The cost of tea a = Rs. 95/kg The cost of tea b = Rs. 100/kg The cost of tea c = Rs. 70/kg

We need to find the quantities of tea a, b, and c that should be blended to produce 100 kg of mixture worth Rs. 90/kg.

Equation 1: x + y + z = 100 (Since the total quantity of the mixture is 100 kg)

Equation 2: (95x + 100y + 70z) / 100 = 90 (Since the total cost of the mixture is Rs. 90/kg)

From the given information, we also know that the quantities of tea b and c are equal, so y = z.

Substituting y = z in Equation 1, we get: x + 2y = 100

Substituting y = z in Equation 2, we get: (95x + 100y + 70y) / 100 = 90 (95x + 170y) / 100 = 90 95x + 170y = 9000

Now, we have a system of equations: x + 2y = 100 95x + 170y = 9000

We can solve this system of equations to find the values of x, y, and z.

Using any suitable method (substitution, elimination, or matrices), we find that the solution is: x = 50, y = 25, z = 25

Therefore, the quantities of tea a, b, and c that should be blended to produce 100 kg of mixture worth Rs. 90/kg are 50 kg, 25 kg, and 25 kg respectively.

Hence, the correct answer is option B) 50, 25, 25.

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