Sita and Geeta are two sisters. If Sita's age is written after Geeta's age a four digit perfect
square (number) is obtained. If the same exercise is repeated after 13 years another four
digit perfect square (number) will be obtained. What is the sum of the present ages of Sita
and Geeta?
Answers
Given : Sita's age is written after Geeta's age a four digit perfect square (number) is obtained
the same exercise is repeated after 13 years another four digit perfect square (number) will be obtained
To Find : sum of the present ages of Sita and Geeta
Solution:
Let say Age of Geeta = AB
Let say age of Sita = CD
ABCD value = 1000A + 100B + 10C + D = perfect Square = x²
same exercise is repeated after 13 years another four digit perfect square (number) will be obtained.
Age of Geeta = AB + 13
age of Sita = CD + 13
now 13 is added in AB and 13 is added in CD
Hence
1000A + 100B + 10C + D + 1300 + 13 = x² + 1313 = y²
y² = x² + 1313
=> (y + x)(y - x) = 1313
=> (y + x)(y - x) = 13 x 101
=> y + x = 101
y - x = 13
y = 57
x = 44
44² = 1936
57² = 3249
AB = 19 CD = 36
AB + 13 = 32 , CD + 13 = 49
Age of Geeta = 19
age of Sita = 36
Sum of their ages = 19 + 36 = 55
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