There are some marbles of two colours black and golden in a jar. If the ratio of the number of black marbles to the golden marbles is 5:3 and the total number of marbles in the jar is 120, then how many black marbles are there in the jar?

Options

A. 45
B. 75
C. 60
D. 80

Answer

To solve the problem step by step, we will follow the given information and use the ratio to find the number of black marbles.

### Step-by-Step Solution:

1. **Understand the Ratio**:
The ratio of the number of black marbles (B) to the number of golden marbles (G) is given as 5:3. This can be expressed as:
\[ \frac{B}{G} = \frac{5}{3} \]

2. **Express in Terms of a Variable**:
Let the number of black marbles be \(5k\) and the number of golden marbles be \(3k\), where \(k\) is a common multiplier.

3. **Set Up the Total Equation**:
The total number of marbles is given as 120. Therefore, we can write the equation:
\[ B + G = 120 \]
Substituting the expressions for B and G, we get:
\[ 5k + 3k = 120 \]

4. **Combine Like Terms**:
Combine the terms on the left side:
\[ 8k = 120 \]

5. **Solve for k**:
To find \(k\), divide both sides by 8:
\[ k = \frac{120}{8} = 15 \]

6. **Find the Number of Black Marbles**:
Now that we have \(k\), we can find the number of black marbles:
\[ B = 5k = 5 \times 15 = 75 \]

7. **Conclusion**:
Therefore, the number of black marbles in the jar is \(75\).

### Final Answer:
The number of black marbles is **75**.

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