Question

Age of Lata is AB and age of Asha is CD. If the digits of their ages are arranged as ABCD then the 4 digit number thus formed is a perfect square of a paticular number.If the same operation is repeated after 11 years then the 4 digit so formed is also a perfect square number of another number.Find the present ages of Asha and Lata.
(Value of A and B may be different)​

Answer 1

Step-by-step explanation:

If the digits of their ages are arranged as ABCD then the 4 digit number thus formed is a perfect square of a paticular number. If the same operation is repeated after 11 years then the 4 digit so formed is also a perfect square number of another number.

Answer 2

Given:

Age of Lata = AB

Age of Asha = CD

ABCD is a four digit perfect square number.

After 11 yrs , combining the digits of the ages of Asha and Lata, we get the perfect square number.

To Find :

Find the ages of Asha and Lata.

Solution:

ABCD = $x^2$.............................................(1)

∵AB is increased by 11, CD is increased by 11,

∴Digits of ABCD gets changed

∴In ABCD ,

A is changed to (A+1), we have to add 1000

B is changed to (B+1), we have to add 100

C is changed to (C+1), we have to add 10

D is changed to (D+1), we have to add 1,

 So in total we have to  add 1000+100+10+1=1111

So, ABCD +1111= $y^2$( new number)......................(2)

Subtracting eq(1) from eq(2), we get

     1111=$y^2-x^2$

     11×101=$(y+x)(y-x)$

      $y+x=101\\y-x=11$

∴ $x=45$

∴ ABCD= $x^2$

             = ${45}^2$

             =$2025$

∴AB=20, CD=25

Hence the age of Lata is 20 yrs and of Asha is 25 yrs.