Three type of Rice mxied together. Their volumes are in the proportion 5,4 and 3 respectively and the weight of equal volunes are in proportion of 6,5 and 4 respectively. What is the wight of the rice of the first type if the wight of the mixture is 248kg ?

Options

A. 120kg
B. 119kg
C. 110kg
D. 118kg

Explanation

To solve the problem step by step, we will follow the given ratios and calculate the weight of the first type of rice in the mixture.

### Step 1: Understand the Ratios
The volumes of the three types of rice are given in the ratio of 5:4:3. This means if we consider the volumes as 5x, 4x, and 3x respectively for the three types of rice.

### Step 2: Assign Weights to Each Type
The weights of equal volumes of the three types of rice are given in the ratio of 6:5:4. This means if we consider the weights as 6y, 5y, and 4y respectively for the three types of rice.

### Step 3: Calculate the Total Weight for Each Type
To find the total weight contributed by each type of rice, we multiply the volume by the weight per unit volume:
- Weight of the first type of rice = Volume of first type × Weight per unit volume = 5x * 6y = 30xy
- Weight of the second type of rice = Volume of second type × Weight per unit volume = 4x * 5y = 20xy
- Weight of the third type of rice = Volume of third type × Weight per unit volume = 3x * 4y = 12xy

### Step 4: Calculate the Total Weight of the Mixture
Now, we can find the total weight of the mixture by adding the weights of all three types of rice:
Total Weight = 30xy + 20xy + 12xy = 62xy

### Step 5: Set Up the Equation
We know from the problem that the total weight of the mixture is 248 kg. Therefore, we can set up the equation:
62xy = 248

### Step 6: Solve for xy
To find the value of xy, we divide both sides of the equation by 62:
xy = 248 / 62
xy = 4

### Step 7: Calculate the Weight of the First Type of Rice
Now that we have the value of xy, we can find the weight of the first type of rice:
Weight of the first type = 30xy = 30 * 4 = 120 kg

### Final Answer
The weight of the rice of the first type is **120 kg**.

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