There are two mixtures containing Gold, silver and platinum. First mixture contains 40% platinum and second mixture contains 26% silver. The percentage of gold in both mixtures are same. If 150 kg of first mixture is mixed with the 250 kg of second mixture, then the percentage of Gold in resultant mixture is 30%. Find the quantity of platinum in the resultant mixture.

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the Variables
Let:
- \( P_1 \) = percentage of platinum in the first mixture = 40%
- \( S_2 \) = percentage of silver in the second mixture = 26%
- \( G \) = percentage of gold in both mixtures (same for both)
- \( M_1 \) = weight of the first mixture = 150 kg
- \( M_2 \) = weight of the second mixture = 250 kg
- \( R \) = percentage of gold in the resultant mixture = 30%

### Step 2: Calculate the Total Weight of the Resultant Mixture
The total weight of the resultant mixture is:
\[ M_{total} = M_1 + M_2 = 150 \, \text{kg} + 250 \, \text{kg} = 400 \, \text{kg} \]

### Step 3: Set Up the Equation for Gold
Since the percentage of gold in the resultant mixture is given as 30%, we can express the weight of gold in the resultant mixture:
\[ \text{Weight of Gold} = R \times M_{total} = 0.30 \times 400 \, \text{kg} = 120 \, \text{kg} \]

### Step 4: Calculate the Remaining Percentages
The total percentage of platinum and silver in both mixtures can be calculated as follows:
- The percentage of platinum in the first mixture is 40%, hence the percentage of silver in the first mixture is \( 100 - (G + P_1) = 100 - (G + 40) \).
- The percentage of silver in the second mixture is given as 26%, hence the percentage of platinum in the second mixture is \( 100 - (G + S_2) = 100 - (G + 26) \).

### Step 5: Set Up the Equation for the Resultant Mixture
The total percentage of platinum and silver in the resultant mixture can be expressed as:
\[ P_1 + S_2 + G = 100 \]
Substituting the values:
\[ 40 + 26 + G = 100 \]
Solving for \( G \):
\[ G = 100 - 66 = 34\% \]

### Step 6: Calculate the Percentage of Platinum in the Resultant Mixture
Now we can find the percentage of platinum in the resultant mixture:
- The total percentage of platinum in the resultant mixture is:
\[ P_{resultant} = \frac{(P_1 \times M_1) + (P_2 \times M_2)}{M_{total}} \]
Where \( P_2 \) is the percentage of platinum in the second mixture, which can be calculated as:
\[ P_2 = 100 - (G + S_2) = 100 - (34 + 26) = 40\% \]

### Step 7: Calculate the Quantity of Platinum
Now we can calculate the total quantity of platinum in the resultant mixture:
\[ \text{Weight of Platinum} = \frac{(40\% \times 150 \, \text{kg}) + (40\% \times 250 \, \text{kg})}{400 \, \text{kg}} \]
Calculating:
\[ \text{Weight of Platinum} = \frac{(0.40 \times 150) + (0.40 \times 250)}{400} = \frac{60 + 100}{400} = \frac{160}{400} = 0.40 \text{ or } 40\% \]

Finally, the quantity of platinum in the resultant mixture is:
\[ \text{Quantity of Platinum} = 0.40 \times 400 \, \text{kg} = 160 \, \text{kg} \]

### Final Answer
The quantity of platinum in the resultant mixture is **160 kg**.

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