Math, asked by sukanyadevnath, 2 months ago

3. 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

Answered by amitnrw
0

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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