1. Given data

• Initial nucleus mass number: $A_i = 242$
• Initial binding energy per nucleon: $7.6\,\text{MeV}$
• It breaks into two fragments, each of mass number $121$
• Binding energy per nucleon of each fragment: $8.1\,\text{MeV}$

2. Total initial binding energy

The total binding energy of the original nucleus is

3. Total final binding energy

Each fragment has mass number $121$, so binding energy of one fragment is

Since there are two identical fragments,

4. Gain in binding energy

The gain in binding energy is

5. Final answer

So, the total gain in binding energy is $121\,\text{MeV}$.