# The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differ by 30 years. Find the ages of Ani and Biju

**Solution:**

We will be using the concept of two-variable linear equations to solve the given question.

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

Therefore, the age of Ani’s father, Dharam is 2x years,

And the age of Biju’s sister Cathy is y/2 years.

**Case (I):** When Ani is older than Biju

The ages of Ani and Biju differ by 3 years,

x - y = 3 ....(1)

The ages of Cathy and Dharam differs by 30 years,

2x - y/2 = 30

4x - y = 60 ....(2)

Subtracting (1) from (2), we obtain

4x - y - (x - y) = 60 - 3

3x = 57

x = 19

Substituting x = 19 in equation (1), we obtain

19 - y = 3

y = 16

Therefore, Ani is 19 years old and Biju is 16 years old.

**Case (II):** When Biju is older than Ani.

The ages of Ani and Biju differ by 3 years,

y - x = 3

- x + y = 3 ....(1)

The ages of Cathy and Dharam differs by 30 years,

2x - y/2 = 30

4x - y = 60 ....(2)

Adding (1) and (2), we obtain

- x + y + 4x - y = 3 + 60

3x = 63

x = 21

Substituting x = 21 in equation (1), we obtain

- 21 + y = 3

y = 24

Therefore, Ani is 21 years old and Biju is 24 years old.

Thus, Ani is 19 years old and Biju is 16 years old or Ani is 21 years old and Biju is 24 years old.

**☛ Check: **NCERT Solutions Class 10 Maths Chapter 3

**Video Solution:**

## The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differ by 30 years. Find the ages of Ani and Biju

NCERT Solutions for Class 10 Maths Chapter 3 Exercise 3.7 Question 1

**Summary:**

The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differ by 30 years. Ani is 19 years old and Biju is 16 years old or Ani is 21 years old and Biju is 24 years old if the ages of two friends Ani and Biju differ by 3 years.

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