Four years ago, the average age of a family of four persons was 18 years. During this period, a baby was born. Today if the average age of the family is still 18 years, the age of the baby is

### Concept & Formula When time passes, every living member's age increases by the same number of years. $$\text{Total Age} = \text{Average Age} \times \text{Number of Members}$$ --- ### Step-by-Step Solution * **Given:** * 4 years ago, 4 members had an average age of 18 years. * Total age 4 years ago = $4 \times 18 = 72\text{ years}$. * **Calculation for Today:** * In 4 years, each of the 4 original members aged by 4 years. * Present total age of these 4 members = $72 + (4 \times 4) = 88\text{ years}$. * Today, there are 5 members (including the baby), and the average age is still 18 years. * Present total age of the 5-member family = $5 \times 18 = 90\text{ years}$. * **Finding the Baby's Age:** * Age of the baby = (Total age of 5 members today) - (Total age of 4 original members today) * Age of the baby = $90 - 88 = 2\text{ years}$. --- ### Exam Strategy & Shortcut * If no baby was born, the average age of the 4 members today would increase by 4 years, becoming $18 + 4 = 22\text{ years}$. * The deficit in the total sum caused by the baby maintaining the average at 18 is: $$4 \times (22 - 18) = 16\text{ years}$$ * The baby brings down the average, meaning the baby's age is: $$18 - 16 = 2\text{ years}$$ --- ### Common Pitfall A frequent error is forgetting to add 4 years to each of the 4 original family members, leading to an incorrect total present age calculation. --- ### Final Answer **Therefore, the correct answer is 2 hours.**