The question asks:

How many kilograms of basmati rice worth ₹96 per kg should be mixed with 15 kg of basmati rice worth ₹80 per kg to obtain a mixture costing ₹90 per kg?

Let's solve this using the method of alligation.

Let:

• $x$ = the quantity of basmati rice worth ₹96 per kg that needs to be mixed.

The goal is to create a mixture where the price is ₹90 per kg.

Step-by-Step Solution:

1. Set up the equation for the total cost:

   • We know that the cost of the mixture will be a weighted average of the two rice prices.

2. Cost per kg formula:

   • Using the weighted average formula, we set up the equation as follows: $\frac{96x + 80 \cdot 15}{x + 15} = 90$

3. Expand and simplify:

   • Multiply both sides by $x + 15$: $96x + 80 \cdot 15 = 90(x + 15)$
   • Expanding this gives: $96x + 1200 = 90x + 1350$

4. Solve for $x$:

   • Bring all terms involving $x$ to one side and constants to the other: $96x - 90x = 1350 - 1200$
   • Simplify: $6x = 150$
   • Divide by 6: $x = 25$

Answer:

You need to mix 25 kg of basmati rice worth ₹96 per kg with 15 kg of basmati rice worth ₹80 per kg to get a mixture costing ₹90 per kg.

Would you like further details on this process or have any other questions?

Related Questions:

1. What is the general formula for a weighted average in mixture problems?
2. How would the answer change if the target cost per kg was different?
3. Can this be solved using the method of alligation directly?
4. What if the price of the other rice was ₹85 per kg instead of ₹80?
5. How do we set up mixture problems if there are more than two types of items?

Tip:

In mixture problems, double-check units and confirm that the weighted average aligns with the desired final cost or concentration.