Question

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​

Answer 1

explanation of the solution ;  Let the ages of Ani, Biju, Dharam and Cathy be a, b, c and d respectively.

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

a – b = 3

c = 2a and b = 2d

c – d = 30

Solving the above four equations

⇒ 2a – b/2 = 30

⇒ 2a – a/2 + 3/2 = 30

⇒ a = 19

Thus, b = 16 years

Answer 2

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Given that

The age difference between Ani and Biju is 3 yrs. 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.

As per the given data two cases can be assumed

Case (i) When Ani is older

Case (ii) When Biju is older

From both the cases we know that that Ani’s father’s age is 30 yrs more than that of Cathy’s age.

To Find out

We have to determine the ages of Ani and Biju.

Solution

Let the ages of Ani be A

Let the age of Biju be B

Hence, the age of Dharam = 2 x A = 2A yrs.

The age of Biju sister Ani B/2 yrs

As per the given conditions will solve

Case (i)

When Ani is older than that of Biju

A – B = 3 – – – – – – – – (1) {older by 3 years}

2A−B/2 = 30

4A – B = 60 – – – – – – – – – – – (2)

By subtracting the equations (1) and (2) we get,

3A = 60 – 3 = 57

A = 57/3 = 19

The age of Ani = 19 yrs

The age of Biju is 19 – 3 = 16 yrs.

Case (ii)

When Biju is older than Ani,

B – A = 3 – – – – – – – – – (1) {older by 3 years}

2A − B/2 = 30

4A – B = 60 – – – – – – – – – (2)

Adding the equation (1) and (2) we get,

3A = 63

A = 21

Answer

The age of Ani is 21 yrs

The age of Biju is 21 + 3 = 24 yrs.