Rizwan has a box In which he kept red and blue marbles. The red marbles and blue marbles were In the ratio `5 : 4`. After he lost 5 red marbles, the ratio became `10 : 9`. How many marbles does he have now?

Options

A. 81
B. 86
C. 76
D. 91

Answer

To solve the problem step by step, we will follow the information provided and use algebra to find the total number of marbles Rizwan has now.

### Step 1: Define Variables
Let the number of red marbles be \(5x\) and the number of blue marbles be \(4x\). This is based on the initial ratio of red to blue marbles, which is \(5:4\).

### Step 2: Set Up the Equation After Losing Marbles
After Rizwan loses 5 red marbles, the number of red marbles becomes \(5x - 5\). The new ratio of red to blue marbles is given as \(10:9\). We can set up the equation based on this ratio:
\[ \frac{5x - 5}{4x} = \frac{10}{9} \]

### Step 3: Cross-Multiply to Solve for \(x\)
Cross-multiplying gives us:
\[ 9(5x - 5) = 10(4x) \]
Expanding both sides:
\[ 45x - 45 = 40x \]

### Step 4: Isolate \(x\)
Now, we will isolate \(x\) by moving all terms involving \(x\) to one side:
\[ 45x - 40x = 45 \]
This simplifies to:
\[ 5x = 45 \]
Dividing both sides by 5 gives:
\[ x = 9 \]

### Step 5: Calculate the Total Number of Marbles
Now that we have \(x\), we can find the total number of marbles. The total number of marbles before losing any is:
\[ 5x + 4x = 9x \]
Substituting \(x = 9\):
\[ 9x = 9 \times 9 = 81 \]
After losing 5 red marbles, the total number of marbles becomes:
\[ 81 - 5 = 76 \]

### Final Answer
Rizwan now has **76 marbles**.

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