Ani and Biju, two pals, are three years apart in age. Dharam, Ani's father, is twice his age, while Biju is twice his sister Cathy's age. Cathy and Dharam are 30 years apart in age. What is the age of Ani and Biju?

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Ani and Biju, two pals, are three years apart in age. Dharam, Ani's father, is twice his age, while Biju is twice his sister Cathy's age. Cathy and Dharam are 30 years apart in age. What is the age of Ani and Biju?

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Ani Age = 19, Biju Age=16 or Ani Age =21, Biju Age=24

Ani Age = 18, Biju Age=15 or Ani Age =20, Biju Age=23

Ani Age = 19, Biju Age=22 or Ani Age =24, Biju Age=27

Ani Age = 18, Biju Age=21 or Ani Age =24, Biju Age=27

answer is A.

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Detailed Solution

Given that Ani and Biju, two pals, are three years apart in age.
Dharam, Ani's father, is twice his age, while Biju is twice his sister Cathy's age.
Also, given Cathy and Dharam are 30 years apart in age.
We may have two cases according to given situation.
Case I – If Cathy is older than Dharam.
Given that Ani and Biju’s age differ by 3 years.
Let x be the age of Ani and y be the age of Biju.
(Consider Ani is older than Biju)
x – y = 3 ---- (1)
Also, Ani’s father Dharam is two times the age of Ani.
Dharam = 2x ---- (i)
Biju is two times the age of Cathy.
y = 2(Cathy)
Cathy

= y 2

---- (ii)
Also, ages of Dharam and Cathy differ by 30 years.
Dharam – Cathy =30
Putting equation (i) & (ii) in the above statement.

2 x − y 2 = 30 ⇒ x − y 4 = 15 -----(2)

Determine the value of ‘y’.
Subtract equation (1) from equation (2).

x − y 4 − (x − y) = 15 − 3 ⇒ y − y 4 = 12 ⇒ 4 y − y 4 = 12 ⇒ 3 y = 48 ⇒ y = 16

Determine the value of ‘x’ from the known value of ‘y’.
Putting the value of y in equation (1).

x − 16 = 3 x = 19

Case II – If Dharam is older than Cathy.
Given that, Ani and Biju’s age differ by 3 years.
Let x be the age of Ani and y be the age of Biju.
(Consider Biju is older than Ani)
y – x = 3 ---- (1)
Also provided Ani’s father Dharam is two times the age of Ani.
Dharam = 2x ---- (i)
Biju is two times the age of Cathy.
y = 2(Cathy)
Cathy

= y 2

---- (ii)
Also, ages of Dharam and Cathy differ by 30 years.
Putting equation (i) & (ii) in the above statement.

2 x − y 2 = 30 ⇒ x − y 4 = 15 ------(2)

Determine the value of ‘y’.
Add equation (1) & (2), we get

y − y 4 − x + x = 3 + 15 ⇒ y − y 4 = 18 ⇒ 3 y = 72 ⇒ y = 24

Determine the value of ‘x’ from the known value of ‘y’,
Putting the value of y in equation (1).

24 − x = 3 ⇒ x = 21

In Case I, the age of Ani is 19 years and the age of Biju is 16 years.
In Case II, the age of Ani is 21 years and the age of Biju is 24 years.
Therefore, option 1 is correct.

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