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 4 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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