Question

the ages of two friends Ani and Biju differ by 3 years and his father Dharam is twice as old as Ani and Biju is twice as old as a sister Cathy the ages of Cathy and Dharam differ by 30 years find the ages of Ani and Biju .​

Answer 1

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Answer 2

Given:-

• The ages of two friends Ani and Biju differ by 3 years. Ani's father Dharam is twice as Ani and Biju is twice as old as his sister Cathy.
• The ages of Cathy and Dhara by 30 years.

To find:-

• Find the ages of Ani and Biju.

Solutions:-

• The difference between the ages of Biju and Ani is 3 years.
• Biju is 3 years older than Ani or Ani is 3 years older. Ani's father age will be 30 years more than of cath's age.

• Let the age of Ani and Biju be x and y year's.

Therefore, age of Ani's father , Dharam = 2 × x = 2x years.

And age of Biju's sister Cathy = y/2 years.

Case 1.

Ani is older than Biju by 3 years.

=> x - y = 3 ........(i).

=> 2x - y/2 = 3

=> 4x - y = 60 .....(ii).

Subtracting (ii). from (i). we get

${4x} \: - \: {y} \: \: = \: \: {60} \\ {x} \: - \: {y} \: \: = \: \: {3} \\ \underline{ - \: \: \: \: \: \: \: \: + \: \: \: \: \: \: \: \: = \: \: \: \: \: \: - \: \: \: \: \: \: \: \: \: } \\ \: {3x} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \: \: \: {57}$

=> x = 57/3

=> x = 19

Therefore, age of Ani = 19 years and age of Biju = 19 - 3 = 16 years.

Case 2.

Biju is older than Ani.

=> y - x = 3 .......(i)

=> 2x - y/2 = 30

=> 4x - y = 60 ......(ii).

Subtracting (ii). from (i). we get

${4x} \: - \: {y} \: \: = \: \: {60} \\ {-x} \: + \: {y} \: \: = \: \: {3} \\ \underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \: {3x} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \: \: \: {63}$

=> x = 63/3

=> x = 21

Therefore, age of Ani = 21 years.

And age of Biju = 21 + 3 = 24 years.