Question

the ages of two friends Ani and Biju differ by 3 years and 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 the dharam differ by 30 years find the ages of Ani and Biju

Answer 1

SOLUTION:

Let the age of Ani and Biju be 'a' years and

Let the age of Biju be 'b' years

Now,

According to the question,

⇒ a - b = ±3   -------(i)

[We don't know whether a > b  or b > a]

Also,

The age of Ani's father Dharam = '2a' years

And

The age of Biju sister = $\frac{b}{2}\ years$

Now,

From the question,

$2a - \frac{b}{2}= 30$

⇒ 4a - b = 60  ------(2)

• CASE 1

When, a - b = 3  -----(3)

Now, by subtracting equation(3) from equation(2), we will get,

⇒ 3a = 57

⇒ a = 19

Now

Putting x = 19 in equation(3), we will get,

⇒ 19 - b = 3

⇒ b = 16

• CASE 2

When,

a - b = -3 ----(4)

By subtracting equation(4) from equation(2), we will get,

⇒ 3a = 60 + 3

⇒ 3a = 63

⇒ a = 21

Now,

By putting the value of a = 21 in equation (4), we will get,

⇒ 21 - b = -3

⇒ - b = -3 - 21

⇒ - b = -24

⇒ b = 24

Hence,

The age of Ani is 19 years

And the age of Biju is 16 years

Or

The age of Ani is 21 years

And the age of Biju is 24 years.

Answer 2

$\huge{\mathcal{\underline{\green{Answer}}}}$

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.