Question

The ages of two friends Ani and Biju differ by 3 years . Ani' s father Dharam istwice 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

Let age of ani =a, biju=b, cathy =c, dharam =d.
there are 2 cases, lets say Ani is elder than Biju  , case 2 would be Biju is elder than Ani,
Try that too, but lets take in case 1.                    
a-b = 3
d=2a
b=2c
d-c=30
substituting
(2a -b/2)2=30*2
a-b=3
now
    4a - b = 60
  -  a   - b = 3
     3a = 57
a= 19, as biju is smaller than ani, b=16, d=2a, so d=38, c=b/2 so c=8years.
You could take ani as smaller than biju, but u would get it wrong and dharam is father of ani , so will be bigger than biju and cathy.
now d-c = 30, as 38-8= 30
so you may get it wrong on  first attempt , but see to it that u try both cases.

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.