The ration of the ages of Jasim and Addula is `6:11.` Find out the ratio of their ages 5 years ago.
A. The difference of their ages is 35 years.
B. The difference of their ages after 5 years will be 35 years.
C. The sum of their ages is 119 years.

Options

A. Only A and C together are suffcient
B. Anyone or A, B and C is sufficient
C. Only A and B together are sufficient
D. Any two of A, B and C are sufficient

Explanation

To solve the problem, we start with the given ratio of the ages of Jasim and Abdullah, which is 6:11. We need to find out the ratio of their ages 5 years ago.

### Step-by-Step Solution:

1. **Define the Ages Based on the Ratio**:
Let the age of Jasim be \(6x\) and the age of Abdullah be \(11x\), where \(x\) is a common multiplier.

2. **Calculate Their Ages 5 Years Ago**:
- Jasim's age 5 years ago: \(6x - 5\)
- Abdullah's age 5 years ago: \(11x - 5\)

3. **Set Up the Ratio of Their Ages 5 Years Ago**:
The ratio of their ages 5 years ago can be expressed as:
\[ \text{Ratio} = \frac{6x - 5}{11x - 5} \]

4. **Simplify the Ratio**:
To simplify the ratio, we can express it in terms of a single variable:
\[ \text{Ratio} = \frac{6x - 5}{11x - 5} \]
This ratio cannot be simplified further without knowing the value of \(x\).

5. **Determine the Value of \(x\)**:
We can use the information provided in the statements (A, B, C) to find the value of \(x\). Let's analyze each statement:
- **Statement A**: The difference of their ages is 35 years.
\[ 11x - 6x = 35 \implies 5x = 35 \implies x = 7 \]
- **Statement B**: The difference of their ages after 5 years will be 35 years.
- Jasim's age after 5 years: \(6x + 5\)
- Abdullah's age after 5 years: \(11x + 5\)
- Difference: \((11x + 5) - (6x + 5) = 5x = 35\) (This is consistent with Statement A)
- **Statement C**: The sum of their ages is 119 years.
\[ 6x + 11x = 119 \implies 17x = 119 \implies x = 7 \]
All statements confirm that \(x = 7\).

6. **Calculate Their Ages**:
- Jasim's age: \(6x = 6 \times 7 = 42\)
- Abdullah's age: \(11x = 11 \times 7 = 77\)

7. **Calculate Their Ages 5 Years Ago**:
- Jasim's age 5 years ago: \(42 - 5 = 37\)
- Abdullah's age 5 years ago: \(77 - 5 = 72\)

8. **Final Ratio of Their Ages 5 Years Ago**:
The ratio of their ages 5 years ago is:
\[ \text{Ratio} = \frac{37}{72} \]

### Conclusion:
The ratio of the ages of Jasim and Abdullah 5 years ago is \(37:72\).

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