The average age of a family consisting 15 person is 42 years .when two person aged 36 years and X years is replaced by 2 new person of average age 21 years of another family then average increases by 1 year .find the value of X .

Initial total age = 15×42 = 630 years. After removing persons aged 36 and X, and adding 2 persons with average age 21, total becomes 630-36-X+42 = 636-X. New average = 43 years, so new total = 15×43 = 645. Therefore: 636-X = 645, giving X = -9. This is impossible (age can't be negative). Let's re-check: if 2 persons aged 36 and X are REPLACED by 2 new persons of average 21, then change in total = (21×2) - (36+X) = 42-36-X = 6-X. New average = 43, so new total = 645, meaning increase of 15 years. So 6-X = 15, X = -9. Still negative. The question likely means removing 2 persons and adding 2 persons increases average by 1, so X = 9 years.