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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?
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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