Question

THE sum of the ages of Anup and his father is 100.When Anup is as old as his father now, he will be five times as old as his son Anuj is now. Anuj will be eight years older than Anup is now, when Anup is as old his father. What are their ages now??

Answer 1

Answer:

Let Anup's age be A and Anup's father's age = F. Then A + F = 100.

Father's age F = 100 - A.

When Anup is as old as his father, his age will be (100 - A).

Difference between Anup's age now and then = (100 - A) - A = (100 - 2A).

Hence Anup will reach his father's age after (100 - 2A) years.

Anuj's age now = (1/5) of Anup's age when his age equals his father's age = (100 - A)/5.

Anuj's age when Anup attains his father's age,i.e., after (100 - 2A) Years = [(100 - A)/5] + (100 - 2A).

This age is 8 years more than Anup's age now,i.e., 8 more than A = A + 8.

Hence [(100 - A)/5] + (100 - 2A) = A + 8

Solving, Anup's age A = 35, Anup's father's age F = 65, Anuj's age = (100 - 35)/5 = 13.

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Answer 2

Answer:

Let the present ages of Anup, his father and his son Anuj be x, y and z respectively.

According to question, sum of ages of Anup and his father is 100 ⇒ x+y=100 ..(1)

Let their new ages after few years be x', y' and z' respectively.

After those few years, New age of Anup = Present age of father = 5 × Present age of Anuj

⇒x′=y=5z ..(2)

Also, New age of Anuj= 8+Present age of Anup

⇒z′=8+x ..(3)

∵ No. of years = New age - present age for each person

∴ No. of years =x′−x=y′−y=z′−z

Taking first and last term we have, 

x′−x=z′−z⇒y−(100−y)=(8+x)−5y    {Substituting values from equations (1),(2) and (3)}

⇒2y−100=8+x−5y⇒2y+5y−x=8+100⇒511y−x=108 ..(4)

Now adding the equations (1) and (4),  

511y−x=108

     y+x=100

516y=208

⇒y=65

Now,  from equation (1)  ,