Question

1. 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

Answer:

The age of Ani is 19 years

The age of Biju is 16 years .

Step-by-step explanation:

Given as :

The present age of Ani = A years

The present age of Biju = B years

Statement I

The ages of two friends Ani and Biju differ by 3 years.

i.e A - B = 3                .......1

statement II

Ani's father Dharam is twice as old  as Ani

D = 2 A                      ........2

statement III

Biju is twice as old as his sister Cathy

i.e B = 2 C                    .......3

statement IV

The ages of Cathy and Dharam differ  by 30 years

 D - C = 30                 .........4

From 2 and  3 , and 4

2 A  - C = 30    

Or, 2 A -  $\dfrac{B}{2}$   = 30

i.e 4 A - B = 60              ....5

Solving eq 1 and eq 5

( 4 A - B) - (A - B ) = 60 - 3

Or, ( -B + B ) + ( 4 A -  A) = 57

Or, 0 + 3 A = 57

∴  A = 19 years

So, The age of Ani = A = 19 years

Put the value of A in eq 1

 19 - B = 3  

Or, B = 19 - 3

∴  B = 16 years

So, The age of Biju = B = 16 years

Hence, The age of Ani is 19 years and The age of Biju is 16 years . Answer

Answer 2

Answer:

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

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.