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 bom 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 Rameshs age was equal to sum of the ages of Mahesh and Dinesh. What is the age of Ms. Kalpana?a)41 years b)40 years c)39 years d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?

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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 bom 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 sum of the ages of Mahesh and Dinesh. What is the age of Ms. Kalpana?

a)
41 years
b)
40 years
c)
39 years
d)
None of the above

Correct answer is option 'C'. Can you explain this answer?

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Fifteen years back, Ms. Kalpana had three sons Ramesh, Suresh and Raje...

Let G, S, R & N be their ages 15 years back. Let Amit & Keshav be born after x & y years, Thus their ages after 15 years can be written as Ax & K – y respectively. Thus the following equations are formed:
G = 2 (S + R + N)……………………..(1)
2(G + 15) = (S + 15) + (R + 15) + (N + 15) + {A + (15 x)}+ {K + (15 - y) }.....(2)
S + 15 = {A + (15 - x)}+ {K + (15 - y)}........(3)
G + 15 = (S + 15) + (R + 15).......(4)
Substituting equation 3 in 2 & then equation 4 in the new equation formed, we get R = N. Thus G = 24.
Therefore G’s present age is 24 + 15 = 39 years.

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Fifteen years back, Ms. Kalpana had three sons Ramesh, Suresh and Raje...

Age of Ms. Kalpana: 39 years

Explanation:
Given:
1. Fifteen years back, Ms. Kalpana had three sons Ramesh, Suresh, and Rajesh.
2. The sum of the age of Ramesh, Suresh, and Rajesh was equal to half of the age of their mother.
3. After five years, Mahesh was born. Then the age of Ms. Kalpana was equal to the sum of the ages of all her children.
4. Years passed and Dinesh was born, and the age of Ramesh equaled the sum of the ages of Rajesh and Mahesh.
5. The sum of the ages of Ramesh, Suresh, Rajesh, Mahesh, and Dinesh was double the age of their mother.
6. The sum of the ages of Ramesh, Suresh, and Rajesh was also equal to the sum of the ages of Suresh and Ramesh.
7. Ramesh's age was equal to the sum of the ages of Mahesh and Dinesh.

Let's solve the problem step by step:

Step 1: Fifteen years back
Let's assume the age of Ms. Kalpana fifteen years back was x years.
So, the age of Ramesh, Suresh, and Rajesh fifteen years back was (x - 15) years each.

Step 2: After five years, Mahesh was born
After five years, the age of Ms. Kalpana would be (x + 5) years.
The age of Ramesh, Suresh, and Rajesh after five years would be (x - 10) years each.
The age of Mahesh would be 5 years.

Step 3: Years passed and Dinesh was born
Let's assume the age of Ms. Kalpana after Dinesh was born is Y years.
So, the age of Ramesh would be (Y - 5) years.

Step 4: The sum of the ages of Ramesh, Suresh, Rajesh, Mahesh, and Dinesh was double the age of their mother
According to the given condition, (x - 10) + (x - 15) + (x - 10) + 5 + (Y - 5) = 2Y.
Simplifying the equation, we get 3x - 30 + Y - 5 = 2Y.
Combining like terms, we get 3x - 35 = Y.

Step 5: The sum of the ages of Ramesh, Suresh, and Rajesh was equal to the sum of the ages of Suresh and Ramesh
According to the given condition, (x - 10) + (x - 15) + (x - 10) = (x - 10) + (Y - 5).
Simplifying the equation, we get 3x - 35 = x - 5.
Combining like terms, we get 2x = 30.
Solving for x, we get x = 15.

Step 6: Calculate the age of Ms. Kalpana
Substituting the value of x in the equation from Step 5, we get 2(15)

Answered by Wizius Careers · View profile

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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 bom 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 sum of the ages of Mahesh and Dinesh. What is the age of Ms. Kalpana?a)41 years b)40 years c)39 years d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about 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 bom 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 sum of the ages of Mahesh and Dinesh. What is the age of Ms. Kalpana?a)41 years b)40 years c)39 years d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 bom 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 sum of the ages of Mahesh and Dinesh. What is the age of Ms. Kalpana?a)41 years b)40 years c)39 years d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?.

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