In what ratio must a grocer mix two varieties of pulses costing Rs.15 and Rs. 20 per kg respectively to obtain a mixture worth Rs.16.50 per Kg?a)3:7b)7:3c)6:4d)4:6Correct answer is option 'B'. Can you explain this answer?

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Answer

Answer

Problem:
The grocer wants to mix two varieties of pulses costing Rs.15 and Rs.20 per kg respectively to obtain a mixture worth Rs.16.50 per kg. In what ratio must the grocer mix the two varieties of pulses?

Solution:
Let's assume that the grocer mixes x kg of the first variety of pulses and y kg of the second variety of pulses to obtain a total mixture of (x+y) kg.

Step 1: Setting up the equation:
The cost of the first variety of pulses is Rs.15 per kg, so the total cost of x kg of the first variety of pulses would be 15x.
Similarly, the cost of the second variety of pulses is Rs.20 per kg, so the total cost of y kg of the second variety of pulses would be 20y.

The total cost of the mixture is given as Rs.16.50 per kg, so the total cost of the (x+y) kg mixture would be 16.50(x+y).

We can now set up the equation:
15x + 20y = 16.50(x+y)

Step 2: Simplifying the equation:
Let's simplify the equation by expanding the brackets:
15x + 20y = 16.50x + 16.50y

Now, let's move all the terms with x to one side and all the terms with y to the other side:
15x - 16.50x = 16.50y - 20y
-1.50x = -3.50y

Step 3: Finding the ratio:
To find the ratio of x to y, we can divide both sides of the equation by -3.50:
x/y = -3.50/-1.50
x/y = 7/3

Therefore, the ratio in which the grocer must mix the two varieties of pulses is 7:3.

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