The ratio of the density of 3 kinds of petrol `P_1`, `P_2` and `P_3` is 9 : 7 : 5. The density of `P_1` is 18 gm/cc and `P_1`, `P_2` and `P_3` are mixed in the ratio of 6 : 5 : 4 by weight. If a litre of `P_3` cost ₹ 40, then find the cost of `P_3` in 450 kg of mixture of `P_1`, `P_2` and `P_3` :

Options

A. ₹ 380
B. ₹ 480
C. ₹ 355
D. ₹ 448

Answer

To solve the problem step by step, we will break it down into manageable parts:

### Step 1: Understand the given ratios and densities
The ratio of the densities of petrol `P1`, `P2`, and `P3` is given as 9:7:5. We know that the density of `P1` is 18 gm/cc.

### Step 2: Calculate the densities of `P2` and `P3`
Using the ratio of densities:
- Density of `P1` = 9 parts = 18 gm/cc
- Density of `P2` = (7/9) * 18 gm/cc = 14 gm/cc
- Density of `P3` = (5/9) * 18 gm/cc = 10 gm/cc

### Step 3: Determine the total weight of the mixture
The petrols are mixed in the ratio of 6:5:4 by weight. The total parts in this mixture = 6 + 5 + 4 = 15 parts.

### Step 4: Calculate the weight of each type of petrol in the mixture
Given the total weight of the mixture = 450 kg:
- Weight of `P1` = (6/15) * 450 kg = 180 kg
- Weight of `P2` = (5/15) * 450 kg = 150 kg
- Weight of `P3` = (4/15) * 450 kg = 120 kg

### Step 5: Convert the weight of `P3` to volume
We know the density of `P3` is 10 gm/cc. To convert the weight of `P3` to volume:
- Weight of `P3` = 120 kg = 120,000 gm
- Volume of `P3` = Weight / Density = 120,000 gm / 10 gm/cc = 12,000 cc

### Step 6: Convert volume from cc to liters
Since 1 liter = 1000 cc:
- Volume of `P3` in liters = 12,000 cc / 1000 = 12 liters

### Step 7: Calculate the cost of `P3`
The cost of `P3` is given as ₹40 per liter:
- Total cost of `P3` = 12 liters * ₹40/liter = ₹480

### Final Answer
The cost of `P3` in 450 kg of the mixture of `P1`, `P2`, and `P3` is ₹480.

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