Sachin bought 1.5 kg fresh grapes. The ratio of water is to pulp was 4 : 1. When his naughty child crushed these grapes, then some water get wasted. Now the ratio of water is to pulp is 3 : 2. What is the total amount of the crushed grapes?

Options

A. 0.5 kg
B. 1 kg
C. 0.75 kg
D. none of these

Answer

To solve the problem step by step, we will first determine the initial amounts of water and pulp in the grapes, then find the new amounts after the grapes are crushed, and finally calculate the total amount of crushed grapes.

### Step 1: Determine the initial amounts of water and pulp

Given:
- Total weight of grapes = 1.5 kg
- Ratio of water to pulp = 4:1

Let the amount of water be \(4x\) and the amount of pulp be \(x\).

The total amount of grapes can be expressed as:
\[ 4x + x = 1.5 \text{ kg} \]
\[ 5x = 1.5 \text{ kg} \]

Now, solve for \(x\):
\[ x = \frac{1.5}{5} = 0.3 \text{ kg} \]

Thus, the amounts are:
- Water = \(4x = 4 \times 0.3 = 1.2 \text{ kg}\)
- Pulp = \(x = 0.3 \text{ kg}\)

### Step 2: Determine the new ratio after crushing

After the grapes are crushed, the ratio of water to pulp changes to 3:2.

Let the new amount of water be \(W'\) and the amount of pulp remains the same, which is \(0.3 \text{ kg}\).

According to the new ratio:
\[ \frac{W'}{0.3} = \frac{3}{2} \]

Cross-multiply to find \(W'\):
\[ 2W' = 3 \times 0.3 \]
\[ 2W' = 0.9 \]
\[ W' = \frac{0.9}{2} = 0.45 \text{ kg} \]

### Step 3: Calculate the total amount of crushed grapes

The total amount of crushed grapes is the sum of the new amount of water and the amount of pulp:
\[ \text{Total crushed grapes} = W' + \text{Pulp} \]
\[ \text{Total crushed grapes} = 0.45 \text{ kg} + 0.3 \text{ kg} = 0.75 \text{ kg} \]

### Final Answer
The total amount of the crushed grapes is **0.75 kg**.

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