Shortcut Trick Total current age of 5 members = 5 × 20 = 100 years. Total age of the family 5 years ago = 100 − (5 × 5) = 75 years. Number of members just before birth = 5 − 1 = 4 members. Average age just before birth = 75 ÷ 4 = 18.75 years. ∴ The correct answer is 18.75 years. Alternate Method Given: Current number of members = 5 Current average age = 20 years Age of the youngest member = 5 years Formula Used: Total Sum of Ages = Average Age × Number of Members Average Age = Total Sum ÷ Count of Members ⇒ Total present age of all 5 members = 5 × 20 = 100 years ⇒ Since we need the average 5 years ago (at the time of birth), each member was 5 years younger. ⇒ Total reduction in age sum = 5 members × 5 years = 25 years ⇒ Sum of ages of the family 5 years ago = 100 − 25 = 75 years ⇒ Number of members just before the birth = 5 − 1 = 4 members ⇒ Required average age = 75 ÷ 4 = 18.75 years ∴ The correct answer is 18.75 years. Related Concepts: Effect of Time on Average Age If everyone in a group of 'n' people ages by 'x' years, the average age of the group also increases by exactly 'x' years. Birth/Death and Average When a member is added (birth) or removed (death), the total sum changes by their age, and the divisor (number of members) must be updated accordingly. General Formula New Average = (Old Sum ± Change in Sum) ÷ (Old Count ± Change in Count).