There are three baskets of fruits. First basket has twice the number of fruits in the 2nd basket. Third basket has `3/4`th of the fruits in the first. The average of the fruits in all the baskets is 30. What is the number of fruits in the first basket ?

Options

A. 20
B. 30
C. 35
D. 40

Explanation

To solve the problem step by step, let's denote the number of fruits in the second basket as \( x \).

### Step 1: Define the number of fruits in each basket
- **Second Basket**: \( x \)
- **First Basket**: Since the first basket has twice the number of fruits in the second basket, it will have \( 2x \).
- **Third Basket**: The third basket has \( \frac{3}{4} \) of the fruits in the first basket, so it will have \( \frac{3}{4} \times 2x = \frac{3}{2}x \).

### Step 2: Write the equation for the average
The average number of fruits in all three baskets is given as 30. The average can be calculated by taking the total number of fruits and dividing it by the number of baskets (which is 3):

\[ \text{Average} = \frac{\text{Total number of fruits}}{\text{Number of baskets}} = 30 \]

The total number of fruits can be expressed as:

\[ \text{Total} = x + 2x + \frac{3}{2}x \]

### Step 3: Combine the expressions
Now, let's simplify the total:

\[ \text{Total} = x + 2x + \frac{3}{2}x = 3x + \frac{3}{2}x \]

To combine \( 3x \) and \( \frac{3}{2}x \), we can convert \( 3x \) into a fraction with a common denominator:

\[ 3x = \frac{6}{2}x \]

So now we have:

\[ \text{Total} = \frac{6}{2}x + \frac{3}{2}x = \frac{9}{2}x \]

### Step 4: Set up the equation for the average
Now we can set up the equation for the average:

\[ \frac{\frac{9}{2}x}{3} = 30 \]

### Step 5: Solve for \( x \)
To eliminate the fraction, multiply both sides by 3:

\[ \frac{9}{2}x = 90 \]

Now, multiply both sides by \( \frac{2}{9} \):

\[ x = 90 \times \frac{2}{9} = 20 \]

### Step 6: Find the number of fruits in the first basket
Now that we have \( x = 20 \), we can find the number of fruits in the first basket:

\[ \text{First Basket} = 2x = 2 \times 20 = 40 \]

### Final Answer
The number of fruits in the first basket is **40**.

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