A and B share some marbles in the ratio 4 : 5. If B gets 10 marbles more than A, , find the total number of marbles.

Answer

To solve the problem of how A and B share marbles in the ratio of 4:5, where B has 10 more marbles than A, we can follow these steps:

### Step 1: Define the ratio
The ratio of marbles that A and B share is given as 4:5. This means:
- A's share = 4 parts
- B's share = 5 parts

### Step 2: Assign variables
Let the common multiple be represented by \( x \). Therefore:
- A's marbles = \( 4x \)
- B's marbles = \( 5x \)

### Step 3: Set up the equation based on the information given
According to the problem, B has 10 more marbles than A. We can express this as:
\[ 5x = 4x + 10 \]

### Step 4: Solve for \( x \)
Now, we will solve the equation:
\[ 5x - 4x = 10 \\ x = 10 \]

### Step 5: Calculate the number of marbles for A and B
Now that we have the value of \( x \), we can find the number of marbles each person has:
- A's marbles = \( 4x = 4 \times 10 = 40 \)
- B's marbles = \( 5x = 5 \times 10 = 50 \)

### Step 6: Calculate the total number of marbles
Finally, we can find the total number of marbles by adding A's and B's marbles together:
\[ \text{Total marbles} = A's \, marbles + B's \, marbles = 40 + 50 = 90 \]

### Final Answer
The total number of marbles is **90**.

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