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Question

42 litres of milk at ₹25 per litre is mixed with 28 litres of milk at ₹40 per litre. Find the average price of the mixture.

The correct answer is

₹31

To find the average price of the mixture of two different types of milk, we can use the formula for the weighted average of the prices. The weighted average formula is:

\(\text{Average Price} = \frac{(P_1 \times Q_1) + (P_2 \times Q_2)}{Q_1 + Q_2}\)

  • \(P_1\) is the price per litre of the first type of milk, which is ₹25.
  • \(Q_1\) is the quantity of the first type of milk, which is 42 litres.
  • \(P_2\) is the price per litre of the second type of milk, which is ₹40.
  • \(Q_2\) is the quantity of the second type of milk, which is 28 litres.

Now, substituting the values into the formula:

\(\text{Average Price} = \frac{(25 \times 42) + (40 \times 28)}{42 + 28}\)

Calculate the individual products:

  • \(25 \times 42 = 1050\)
  • \(40 \times 28 = 1120\)

Add these products:

\(1050 + 1120 = 2170\)

Add the quantities:

\(42 + 28 = 70\)

Now, divide the total cost by the total quantity to find the average price:

\(\text{Average Price} = \frac{2170}{70} = 31\)

Thus, the average price of the mixture is ₹31.

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Important Questions from Mixture and Alligation

  1. My father is presently 25 years older than me. The sum of our ages 5 years ago was 39 years. Find my present age.

  2. Rice worth ₹43/kg and ₹67/kg are mixed with a third variety in the ratio 2 : 1 : 5. If the mixture is worth ₹96/kg, the price (in ₹) of the third variety of rice per kg will be:

  3. 15 kg of ₹10 per kg wheat is mixed with 5 kg of another type of wheat to get a mixture costing ₹30 per kg. Find the price (per kg) of the costlier wheat.

  4. If a + b + c = 0, then the value of (a² + b² + 2ab) is equal to:

  5. Simplify:

    25 - (18 - 4 × 9 ÷ 3)

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