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  • 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.

Q1.    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.

Answers (1)

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Let the age of Ani be a, age of Biju be b,

Case 1: when Ani is older than Biju

age of Ani's father Dharam:

  d=2a and

age of his sister Cathy :

c=\frac{b}{2}

Now According to the question,

a-b=3...........(1)

Also,

\\d-c=30 \\\Rightarrow 2a-\frac{b}{2}=30

\Rightarrow 4a-b=60..............(2)

Now subtracting (1)  from (2), we get,

3a=60-3

\Rightarrow a=19

putting this in (1)

19-b=3

\Rightarrow b=16

Hence the age of Ani and Biju is 19 years and 16 years respectively.

Case 2:

b-a=3..........(3)

And

\\d-c=30 \\\Rightarrow 2a-\frac{b}{2}=30

\Rightarrow 4a-b=60..............(4)

Now Adding (3) and (4), we get,

3a=63

\Rightarrow a=21

putting it in (3)

b-21=3

\Rightarrow b=24.

Hence the age of Ani and Biju is 21 years and 24 years respectively.

Posted by

Pankaj Sanodiya

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