The average age of the mother and her two sons is 40 years and that of two sons is 30 years. Find the mother’s age?

\$"Average" = "sum of set of numbers" / "amount of numbers in set"\$

The average age of the mother and her two sons = 40 years

\$"Sum of their ages"/3 = 40\$

Multiply with 3 on both sides

⇒ \$\cancel3^1 \times ("Sum of their ages")/\cancel3^1 = 40 \times 3\$

Sum of their ages = 120 years

The average age of two sons = 30 years

\$"Sum of the ages of two sons"/2 = 30\$

Multiply with 2 on both sides

⇒ \$\cancel2^1 \times ("Sum of the ages of two sons")/\cancel2^1 = 30 \times2\$

Sum of their ages = 60 years

Mothers age = 120 - 60 = 60 years

Therefore, the Mothers age is 60 years.