What is the present age of Tanya?

• I. The ratio between the present ages of Tanya and her brother Rahul is 3 : 4 respectively.
• II. After 5 years the ratio between the ages of Tanya and Rahul will be 4 : 5.
• III. Rahul is 5 years older than Tanya.

(a) I and II only

(b) II and III only

(c) I and III only

(d) All I, II and III

(e) Any two of the three

To determine Tanya's present age, let's analyze the information given in the statements.

Statement Analysis

Statement I

The ratio of Tanya's age to Rahul's age is 3:4. This means if we let Tanya's age be 3x, then Rahul's age would be 4x.

Statement II

In 5 years, the ratio of their ages will be 4:5. This can be expressed as:

• Tanya's age in 5 years: 3x + 5
• Rahul's age in 5 years: 4x + 5

Setting up the equation:

(3x + 5) / (4x + 5) = 4/5

Statement III

Rahul is 5 years older than Tanya. This gives us the equation:

Rahul's age = Tanya's age + 5, or 4x = 3x + 5, leading to x = 5.

Combining the Information

Using x = 5, we find:

• Tanya's age = 3x = 15 years
• Rahul's age = 4x = 20 years

Conclusion

All three statements provide consistent information to determine Tanya's age. Therefore, the correct answer is:

(d) All I, II and III