The ratio of number of balls in bags x,y is `2 : 3`. Five balls are taken from bag y and are dropped In bag x. Number of balls are equal In each bag now. Number of balls in each bag now is:

Options

A. 45
B. 20
C. 30
D. 25

Answer

To solve the problem step by step, we will follow the information given in the question.

### Step 1: Define the Variables
Let the number of balls in bag X be represented as \( 2k \) and the number of balls in bag Y be represented as \( 3k \). This is based on the ratio of balls in bags X and Y, which is given as \( 2:3 \).

### Step 2: Adjust the Number of Balls
According to the problem, 5 balls are taken from bag Y and added to bag X. Therefore, the new number of balls in bag X becomes:
\[ \text{Balls in bag X} = 2k + 5 \]
And the new number of balls in bag Y becomes:
\[ \text{Balls in bag Y} = 3k - 5 \]

### Step 3: Set Up the Equation
Now, we know that after transferring the balls, the number of balls in both bags is equal. Thus, we can set up the equation:
\[ 2k + 5 = 3k - 5 \]

### Step 4: Solve the Equation
To solve for \( k \), we will rearrange the equation:
1. Subtract \( 2k \) from both sides:
\[ 5 = 3k - 2k - 5 \]
This simplifies to:
\[ 5 = k - 5 \]
2. Now, add 5 to both sides:
\[ 5 + 5 = k \]
Thus:
\[ k = 10 \]

### Step 5: Calculate the Number of Balls in Each Bag
Now that we have the value of \( k \), we can find the number of balls in each bag:
- For bag X:
\[ \text{Balls in bag X} = 2k = 2 \times 10 = 20 \]
- For bag Y:
\[ \text{Balls in bag Y} = 3k = 3 \times 10 = 30 \]

### Step 6: Verify the New Counts After Transfer
After transferring 5 balls from bag Y to bag X:
- New count in bag X:
\[ 20 + 5 = 25 \]
- New count in bag Y:
\[ 30 - 5 = 25 \]

Both bags now have 25 balls.

### Final Answer
The number of balls in each bag now is **25**.

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