The present age of Sameer's mother is three times the present age of Sameer. After 5 years sum of their ages will be 66 years. Find the present age of Sameer

Question

Accepted Answer

To determine the present age of Sameer, we need to use the information provided in the question and apply logical reasoning.

1. **Understanding the Problem:**
   - Let Sameer's present age be $ S $ years.
   - According to the problem, Sameer's mother's present age is three times Sameer's age. Therefore, her age is $ 3S $ years.
   - After 5 years, the sum of their ages will be 66 years.

2. **Setting Up the Equation:**
   - In 5 years, Sameer's age will be $ S + 5 $.
   - In 5 years, his mother's age will be $ 3S + 5 $.
   - The sum of their ages after 5 years is given as 66 years. Therefore, we can set up the equation:
     $$
     (S + 5) + (3S + 5) = 66
     $$

3. **Solving the Equation:**
   - Simplify the equation:
     $$
     S + 5 + 3S + 5 = 66
     $$
     $$
     4S + 10 = 66
     $$
   - Subtract 10 from both sides:
     $$
     4S = 56
     $$
   - Divide both sides by 4:
     $$
     S = 14
     $$

4. **Conclusion:**
   - The present age of Sameer is 14 years, which corresponds to Option 1.

5. **Explanation of Incorrect Options:**
   - **Option 2 (16 years):** If Sameer were 16 years old, his mother would be $ 3 \times 16 = 48 $ years old. In 5 years, their ages would be 21 and 53, respectively, summing to 74, not 66.
   - **Option 3 (12 years):** If Sameer were 12 years old, his mother would be $ 3 \times 12 = 36 $ years old. In 5 years, their ages would be 17 and 41, respectively, summing to 58, not 66.
   - **Option 4 (15 years):** If Sameer were 15 years old, his mother would be $ 3 \times 15 = 45 $ years old. In 5 years, their ages would be 20 and 50, respectively, summing to 70, not 66.

Therefore, the only option that satisfies all the conditions given in the problem is Option 1, where Sameer's present age is 14 years.