A grand father has 3 grandchildren. Age difference of two children among them…

Let A, B and C are ages of the children starting with eldest and ending in youngest.

Given Eldest is three times youngest ⇒ A = 3 × C ----(i)

Also Eldest is two years more than sum of other two ⇒ A = B + C + 2 ----(ii)

From Eq. (i) & (ii)

⇒ 3C = B + C + 2

⇒ 2C – B = 2

⇒ B = 2C - 2

So the ages are A = 3C, B = 2C – 2 and C = C.

Given difference between two of them is 3 years.

⇒ A - B = 3 or A - C = 3 or B - C = 3

⇒ C + 2 = 3 or 2C = 3 or C – 2 = 3

⇒ C = 1 or C = 3/2 or C = 5

For C = 1 ⇒ A = 3 and B = 0 (Not possible)

C = 3/2 is not possible

∴ C = 5 ⇒ A = 15 and B = 8 years.

Age of elder child = 15 years