Mona's father is thrice as old as Mona. After 12 years, his age will be twice that of his daughter. Find the present age of Mona:

Question

Accepted Answer

To determine the present age of Mona, we need to analyze the information given in the question and verify why Option 3 is correct.

1. **Explanation for Option 3 (12 years):**

Let's denote Mona's current age as $ M $ years. According to the problem, Mona's father is thrice as old as Mona. Therefore, Mona's father's current age is $ 3M $ years.

The problem also states that after 12 years, Mona's father's age will be twice that of Mona's age. In 12 years, Mona's age will be $ M + 12 $ and her father's age will be $ 3M + 12 $.

According to the condition given:
   $$
   3M + 12 = 2(M + 12)
   $$

Simplifying the equation:
   $$
   3M + 12 = 2M + 24
   $$

Subtract $ 2M $ from both sides:
   $$
   M + 12 = 24
   $$

Subtract 12 from both sides:
   $$
   M = 12
   $$

Therefore, Mona's present age is 12 years, which corresponds to Option 3.

2. **Explanation for why other options are incorrect:**

- **Option 1 (36 years):** If Mona were 36 years old, her father would be $ 3 \times 36 = 108 $ years old. In 12 years, Mona would be 48, and her father would be 120. This does not satisfy the condition that her father's age should be twice Mona's age after 12 years.

- **Option 2 (24 years):** If Mona were 24 years old, her father would be $ 3 \times 24 = 72 $ years old. In 12 years, Mona would be 36, and her father would be 84. This also does not satisfy the condition that her father's age should be twice Mona's age after 12 years.

- **Option 4 (18 years):** If Mona were 18 years old, her father would be $ 3 \times 18 = 54 $ years old. In 12 years, Mona would be 30, and her father would be 66. This does not satisfy the condition that her father's age should be twice Mona's age after 12 years.

In conclusion, the only option that satisfies the given conditions is Option 3, where Mona's present age is 12 years.