Question

1 The ages of two friends Ani and Biju differ by 3 yr.
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 yr. Find the ages
of Ani and Biju.​

Answer 1

Answer:

Age of Ani =19 years and age of Biju =16 years.

Step-by-step explanation:

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

Then according to the question-

x−y=3..........(i)

Dharam is twice the age of Ani

Hence, age of Dharam =2x

Age of Cathy is half the age of Biju

Then age of Cathy =  y/2

​Then according to the question  

2x−  y/2=30

⇒4x−y=60......(ii)

Subtracting (ii) from (i)

⇒x−y−4x+y=3−60

⇒−3x=−57

⇒x=  -57/-3=19

Substitute the vale of x in (i)

⇒19−y=3

⇒−y=−16

⇒y=16

∴ Age of Ani =19 years and age of Biju =16 years.

Answer 2

Answer:

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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.