Explanation:

- The total age of Amit and Suvarna on 1 January 2015 is 61 years.

- Amit is three years younger than Suvarna, meaning Suvarna's age is Amit's age plus three years.

- Let’s assume Amit's age on 1 January 2015 is $x$. Then Suvarna’s age would be $x+3$.

- According to their total ages, $x+(x+3)=61$.

- Simplifying, $2x+3=61$ leads to $2x=58$, so $x=29$.

- Therefore, Amit is 29, and Suvarna is 32 years old on 1 January 2015.

- To find Suvarna's age on 1 January 2010, subtract 5 years: $32-5=27$.

- Option 1: 27 years

- Option 2: 24 years

- Option 3: 29 years

- Option 4: 32 years

- The correct answer is Option 1: 27 years.