The average age of Ram and his two children is 17 years and the average age of Ram's wife and the same children is 16 years. If the age of Ram is 33 years, the age of his wife is (in years) :

Answer: Option D

According to the question,
$$=\frac{\text{Ram + 2C}}{3}$$
= 17 years
Ram + 2C = 51 years.....(i)
$$=\frac{\text{Wife + 2C}}{3}$$
= 16 years
Wife + 2C = 48 years.....(ii)
If Ram age = 33 years old
Put this value in equation (i)
∴ 2C = 51 - 33
2C = 18 years old.....(iii)
Put this value in equation (ii)
Wife + 18 = 48
Wife = 48 - 18 = 30
wife = 30 years old