Five years after a couple's marriage, a daughter was born. The average age of the family 3 years after the daughter was born is 24 years. Further 3 years later, the sum of ages of the mother and daughter will be 50 years. Find the age of the father at the time of marriage.

ATQ, Let the age of the father and mother at the time of their marriage be 'f' years and 'm' years, respectively. ATQ, The average age of the family 3 years after the daughter was born = 24 years So, total age of the family at the time of the birth of the daughter = 24 * 3 = 72 Or, (f + 8) + (m + 8) + 3 = 72 Or, f + m + 19 = 72 Or, f + m = 53 ....(i) Further 3 years later, the sum of ages of the mother and daughter will be 50 years Also, (m + 8 + 3) + (3 + 3) = 50 Or, m + 11 + 6 = 50 Or, m + 17 = 50 Or, m = 33 years Put the value of m in equation (i), we get f + 33 = 53 Or, f = 20 So, the age of the father at the time of marriage = 20 years.