 Hello and welcome to the session. I am Ashima and I am going to help you with the following problem. Let us understand the problem. The ages of two friends, Ani and Biju differ by three years. Ani's father, Dharam is twice as old as Ani and Biju is twice as old as his sister Kathi. The ages of Kathi and Dharam differ by 30 years. Finally, ages of Ani and Biju. Now, let us write the solution. Let Ani's age is equal to x years. Let Biju's age is equal to y years. It is given to us that difference between their ages is 3 years. So therefore, we have x-y is equal to 3 or y-x is equal to 3. Now, we can see here Ani's father, Dharam is twice as old as Ani. Therefore, since Ani's age is x years, so therefore his father's age that is Dharam's age is equal to twice x years. Now, it is given to us that Biju is twice as old as his sister Kathi. Therefore, Kathi's age is equal to y by 2 years since Biju's age we have assumed to be y years. Now, it is given to us that ages of Kathi and Dharam differ by 30 years. So, we will get our equation as 2x minus y by 2 is equal to 30 or 4x minus y is equal to 60. Therefore, our required two equations are x minus y is equal to 3 or y minus x is equal to 3. Let us name it as number 1 and 4x minus y is equal to 60 that is number 2. Now, when x minus y is equal to 3 subtracting 1 from 2, we get 4x minus x minus y minus of minus y which is equal to 60 minus 3 which implies 3x minus y plus y is equal to 57 which implies this gets cancelled so 3x is equal to 57 which implies x is equal to 57 by 3 which is equal to 19. Therefore, x is equal to 19. Now, substituting x is equal to 19 in equation 1, we get 19 minus y is equal to 3 which implies y is equal to 19 minus 3 or y is equal to 16. Now, when y minus x is equal to 3, we get our equations as y minus x is equal to 3. Let us name it as equation number 3 and 4x minus y is equal to 60. Let us name it as 4. Now, solving equation 3 and 4 putting x is equal to y minus 3 from equation 3 in equation 4 we get our equation 4 is 4x minus y is equal to 60. Now, substituting x is equal to y minus 3, we get 4 multiplied by y minus 3 minus y is equal to 60. Now, solving this equation for y, we get 4y minus 12 minus y is equal to 60 which implies 4y minus y is 3y is equal to 60 plus 12 which implies 3y is equal to 72 which implies y is equal to 72 by 3 which is equal to 24. Therefore, y is equal to 24. Now, substituting y is equal to 24 and x is equal to y minus 3 which implies x is equal to 24 minus 3 which implies x is equal to 21. Hence, Annie's age is 19 years which we have earlier assumed to be x and from case 1 we have got x is equal to 19 and y is equal to 16. So, 19 years and we choose ages 16 years or from case 2 we have got x is equal to 21 and y is equal to 24. So, Annie's age is 21 years, Biju's age is 24 years. I hope you understood this problem. Bye and have a nice day.