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

Answer

To solve the problem, we will define variables for the number of fruits in each basket and set up equations based on the information given.

### Step 1: Define Variables
Let:
- \( x \) = number of fruits in the second basket.
- Then, the number of fruits in the first basket = \( 2x \) (since the first basket has twice the number of fruits in the second basket).
- The number of fruits in the third basket = \( \frac{3}{4} \times (2x) = \frac{3}{2}x \) (since the third basket has three-fourths of the fruits in the first basket).

### Step 2: Set Up the Equation for Average
The average number of fruits in all three baskets is given as 30. The average can be calculated as follows:

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

So, we can write:

\[ 30 = \frac{(2x + x + \frac{3}{2}x)}{3} \]

### Step 3: Simplify the Equation
Combine the terms in the numerator:

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

Now, substituting this back into the average equation:

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

### Step 4: Solve for \( x \)
Multiply both sides by 3 to eliminate the denominator:

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

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

\[ x = 90 \times \frac{2}{9} = 10 \times 2 = 20 \]

### Step 5: Find the Number of Fruits in the First Basket
Now that we have \( x \), we can find the number of fruits in the first basket:

\[ \text{Number of fruits in the first basket} = 2x = 2 \times 20 = 40 \]

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

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