The sum of ages of 55 children born at the intervals of 33 years each is 5050 years. Find out the age of the youngest child?

Dear student,

Let us suppose the the age of the youngest child id 'a'.

Let's say total number of student= n= 55

Let's say the difference of age= d= 33 years

Let's say the sum of ages = Sn= 5050 years

Now if you see, we can write age of all children in terms of a, like

Age of first child= a

Age of second child= a + 33

Age of third child = (a + 33) + 33

Age of fourth child = {(a + 33) + 33} + 33

and so on, so you can observe easily that these ages are in Arithmetic Progression(AP).

Now as you know Sn= n/2{2a+(n-1)d}

Putting the value of each in the above formula:-

5050 = 55/2{2*a + (55 - 1)33}

surprisingly you will get the value of 'a' in negative and age cannot be negative. So there is some fault with question data.

I hope this answer helps you.

Good luck!!

Greetings dear aspirant

The above question is based on Sum on n terms of an Arithmetic Progression (AP). We know the formula for the sum of n terms which is, Sn = n/2 [2a+(n-1)d]. In this question, n=5 (Number of children), a=age of the youngest child, d=the children are born at a regular interval = 3.

50 = 5/2 [2a+(5-1)3]

Upon solving this we obtain a = 3.

Therefore the age of the youngest child is 4.

Hope this helps!!

All the best for your future career