Question

Fifteen years back, Ms. Kalpana had three sons Ramesh, Suresh and Rajesh. The sum of the age of Ramesh, Suresh and Rajesh was equal to half of the age of their mother. It was during the next five years when Mahesh was born. Then the age of Ms. Kalpana was equal to the sum of the ages of all her children. Time went on and years passed and Dinesh was born and age of Ramesh equaled the sum of the ages of Rajesh and Mahesh. Now, it so happened that the sum of the ages of Ramesh, Suresh, Rajesh, Mahesh and Dinesh was double the age of their mother and was also equal to the sum of the ages of Suresh and Ramesh. Also Ramesh's age was equal to the sum of the ages of Mahesh and Dinesh. What is the age of Ms. Kalpana?

• A. 39 years
• B. 42 years
• C. 41 years
• D. none of the above

Hint:

Set the mother's age 15 years back as k, use the first two clues to link k to the number of years before Mahesh was born, then bring in the later conditions to pin down the exact value.

Answer 1

The Correct Option is A

Step 1: Draw a timeline instead of jumping straight to algebra.
Mark 15 years back as the start. At the start, Kalpana has three sons whose ages add up to exactly half her own age.

Step 2: Mark the point where Mahesh appears on the timeline.
A few years later, within the first five years after the start, Mahesh is born. At that exact instant, Kalpana's age equals the combined age of all her children including newborn Mahesh. Turning this into an equation and simplifying using the Step 1 relationship shows that Kalpana's age at the very start of the timeline is exactly 4 times the number of years that passed before Mahesh arrived.

Step 3: Mark the point where Dinesh appears, and the present day.
Later still, Dinesh is born, and by now, the present day, three age relationships hold together: Ramesh equals Rajesh plus Mahesh, the five children's combined age is both double the mother's age and equal to Suresh plus Ramesh, and Ramesh equals Mahesh plus Dinesh. Each relationship becomes one equation connecting the sons' starting ages, the mother's starting age, and the gaps between the marked points on the timeline.

Step 4: Work backward along the timeline.
Solving these equations together, substituting one into the next to remove the sons' individual ages one at a time, pins the mother's starting age at $k=24$ years.

Final Answer:
Adding the 15 years that have passed since the start of the timeline, Kalpana's present age is $24+15=39$ years. \[ \boxed{39 \text{ years}} \]