Aptitude - Problems on Ages - Discussion

Short trick.

5 children born at interval of 3 years in 50 years.
1st child. 1+3 = 4 year.
2nd child. 2+3 = 5 year.
3rd child. 3+3 = 6 year.
4th child. 4+3 = 7 year.
5th child 5+3 = 8 year.
=>who is youngest child of all above this?
=> Ans= 4 years.

Consider A, B, C, D, E are 5 children.

Let the lowest value as 4 for the youngest child.

Start from 4 and add the difference of 3 to each value.
4 + 7+ 10+ 13+ 16 = 50.

First, you notice every 5 children birth in 3 years cap in 50 years what's is the age in the youngest child.

X, (x+3), (x+6), (x+9), (x+12) years.
x+(x+3)+(x+6)+(x+9)+(x+12) = 50.
Then, here it's using the method in adding x in out 5X +30 = 50.
5X= 50-30.
5X= 20, divisible by 5,
X= 4.

(A)+(A+3)+(A+6)+(A+9)+(A+12) =>5A+30.
=> 5A+30 = 50.
=> A = 4.

sum = 50
x,x+3,x+6,x+9,x+12 => eq1.
eq 1 is in arithmetic mean so the average is x+6
average of 5 children is 50/5 = 10,
So, x+6 = 10,
x = 4.

Total sum 50.
Total children 5.
So, 50/5 =10.
Interval each 3,
So, the youngest age 4.

Here, How come 30? Please explain me.

Let the X be the first or Oldest Child born to Uncle “Bhokal”.

Since All the child is born at 3 years later than their elder Siblings
Therefore sequence will be
X( eldest Child)
X-3
X-6
X-9
X-12( youngest Child)
So, finding X value does not mean the youngest child rather it’s the age of the eldest child

Now, as per the question,
Total age of Children = 50
X+X-3+X-6+X-9+X-12=50
Total X’s + Total Numbers= 50
5X-30=50
5X= 50+30
X=80/5
X=16 (Eldest Son Age)
Since Youngest Child came 12 years later than his /her eldest sibling.
So youngest child= X-12= 16-12=4 years

it is in arithmetic progression with a common difference of 3.

So,
Sn = n/2 [2a + (n-1) d],
50 = 5/2 [2a + (5-1)3],
10 = 1/2[2a + 12],
20 = 2a + 12,
8 = 2a.
a = 4.
Where a is the first term or the age of the youngest child.

Let the ages of the 5 children be a, b, c, d, e.

Intervals of 3
i.e if a=3,
b= a+3,
c= a+3+3,
d=a+3+3+3 and e= a+3+3+3+3.

Therefore their sum becomes:
a+a+3+a+3+3+a+3+3+3+a+3+3+3+3 = 50
Then;
5a + 3(10 times) = 50,
5a + 30 = 50.
5a = 50 - 30.
5a =20.
Divide both sides by 5.
5a/5 = 20/5,
a = 4 years.