There are total 36 fruis in a basket in which some are banana and some are Apple .If one fruit is taken out at random and probability of getting an Apple is `(1)/(6)` then find the number of bananas in the basket.

Options

A. A)20
B. B)28
C. C)24
D. D)30

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Problem
We have a total of 36 fruits in a basket, which consists of apples and bananas. We know the probability of selecting an apple is \( \frac{1}{6} \).

### Step 2: Set Up the Probability Equation
The probability of selecting an apple can be expressed as:
\[ P(\text{Apple}) = \frac{\text{Number of Apples}}{\text{Total Number of Fruits}} \]
Given that the total number of fruits is 36, we can write:
\[ P(\text{Apple}) = \frac{A}{36} \]
where \( A \) is the number of apples.

### Step 3: Substitute the Given Probability
We know from the problem that:
\[ P(\text{Apple}) = \frac{1}{6} \]
So we can set up the equation:
\[ \frac{A}{36} = \frac{1}{6} \]

### Step 4: Cross Multiply to Solve for A
Cross-multiplying gives us:
\[ A \cdot 6 = 1 \cdot 36 \]
This simplifies to:
\[ 6A = 36 \]

### Step 5: Solve for A
Now, divide both sides by 6:
\[ A = \frac{36}{6} = 6 \]
So, there are 6 apples in the basket.

### Step 6: Find the Number of Bananas
Since the total number of fruits is 36, we can find the number of bananas \( B \) by using the equation:
\[ A + B = 36 \]
Substituting the value of \( A \):
\[ 6 + B = 36 \]
Now, solve for \( B \):
\[ B = 36 - 6 = 30 \]

### Conclusion
The number of bananas in the basket is \( 30 \).