The ages of Cathy and Dharam differ by 30 years. Find the ages of Ani and Biju.

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The difference between the ages of Biju and Ani is 3 years. Either Biju is 3 years older than Ani or Ani is 3 years older than Biju. However, it is obvious that in both cases, Ani's father's age will be 30 years more than that of Cathy's age.

Let the age of Ani and Biju be x and y years respectively.

Therefore, age of Ani's father, Dharam = 2 × x = 2x years

Biju's sister Cathy And age of = Pair of Linear Equations in Two Variables Exercise 3.7/image002.pngyears

By using the information given in the question,

Case (I) When Ani is older than Biju by 3 years, x - y = 3 (i)

2x -Pair of Linear Equations in Two Variables Exercise 3.7/image002.png= 30

4x - y = 60 (ii)

Subtracting (i) from (ii), we obtain 3x = 60 - 3 = 57

x -Exercise 3.7/image003.png= 19

Therefore, age of Ani = 19 years

And age of Biju = 19 - 3 = 16 years

Case (II) When Biju is older than Ani, y - x = 3 (i)

2x -Pair of Linear Equations in Two Variables Exercise 3.7/image002.png= 30

4x - y = 60 (ii)

Adding (i) and (ii), we obtain 3x = 63

x = 21

Therefore, age of Ani = 21 years

And age of Biju = 21 + 3 = 24 years

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