Aptitude - Problems on Ages - Discussion

2. 

The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?

[A]. 4 years
[B]. 8 years
[C]. 10 years
[D]. None of these

Answer: Option A

Explanation:

Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.

Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50

5x = 20

x = 4.

Age of the youngest child = x = 4 years.


Vincent said: (Aug 26, 2010)  
How did we get 5x = 20 ?

Martin said: (Sep 11, 2010)  
x+3+x+6+x+9+x+12=30

5x+30=50

5x=50-30

5x=20

x=4.

Priya said: (Sep 28, 2010)  
How to form this step : x+3+x+6+x+9+x+12 ?

Gyan said: (Oct 5, 2010)  
Jus Add x+0
X+3
X+6
X+9
X+12

Cherry said: (Oct 7, 2010)  
x+3x+6x+9x+12x=50

x(1+3+6+9+12)=50

x=50/31

x=1.64

If we do the same like this what is that x mean?

Mani Ramani said: (Oct 26, 2010)  
Hi cherry..

you just add all the X first to get 5X then add numbers to get 30.
Then add 5x+30=50
5X=50-30(shift 30 to right side)
5x=20
X=20/5
X=4

Nandish said: (Nov 20, 2010)  
x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50


how 50 come

Prasad Baanu said: (Dec 4, 2010)  
Hai Nandish..., They have already gave in the question that the sum of ages of those boys are 50:-)
so x + (x+3)+ (x+6)+ (x+9)+(x+12) = 50

Nandan said: (Feb 2, 2011)  
If 1st child age x then 3year gap for next child so x+3
5 children = 5x
5x+30=50
5x=50-30
5x=20
x=20/5
x=4
so 4 years

Raj said: (Feb 15, 2011)  
Use arithmetic prog... formula

s=n/2[2a+(n-1)d]

where s=total sum of numbers,n-count the numbers ,d-diff&a-intial no. so they ask intial no i.e a?

s=50,n=5,d=3,a?

50=5/2[2a+12]=>a=4...

Jitu said: (Mar 19, 2011)  
How can I submitt a question?

Jinju said: (Mar 27, 2011)  
We can easily understand if the avg is 8 then youngestg should be less thgan 8. Then after we calculate the validity of remaining values.

Stella said: (Jun 15, 2011)  
Hi cherry, you just see your calculations: x,3x,6x,9x,12x.(wrong)
u have to add x,x+3,x+6,x+9,x+12.(this is the correct format)
now u have to add and get the result ya.

Satheesh said: (Jun 27, 2011)  
It seems these calculation are merely mathematical wise not logic wise. Whats the relation between X and younger child?

Gkgokulan said: (Jul 13, 2011)  
Its simple logic frnds 4+7+10+13+16=50.

Then the answer is 4.

Ishu Subham said: (Aug 4, 2011)  
Let the ages be (x-6), (x-3), (x), (x+3), (x+6).
then sum of ages = 5x
=> 5x = 50
x = 10
youngest = x-6
=4

Sangeetha said: (Aug 5, 2011)  
Thank you ishu subham, very simple and good logic.

Durgesh said: (Aug 11, 2011)  
Avg. of age of 5 children = 50/5 = 10

Now there are 5 no. having sum 50 and avg. as 10 so no. can only be
= (10-6),(10=3),(10),(10+3),(10+6)
=4 , 7 ,10 ,13 ,16

Neeraj Dixit said: (Sep 17, 2011)  
Just go through answer select 4 first will be 4 than 7 than 10, 13, 16 add all five you will get 50.

Vineshgujjari said: (Sep 25, 2011)  
First of all, Raj Thank you very much.

But I want to ask you that is this formula will ramain for all the sums of this type i.e. problems of ages.

Please reply me asap.

Vineshgujjari said: (Sep 25, 2011)  
Since given 5 children=50
let one children be x
given interval 3 each
so x+(x+3)+(x+6)+(x+9)+(x+12)=50
5x+30=50
x=20/5
x=4..

Kumuda said: (Sep 28, 2011)  
Younger means the person who born at last, then who is the last one, according to problem the person x+12. Submit X value in x+12=16.

Can you please any one clear my doubt ?

Srujan said: (Oct 12, 2011)  
@kumuda sub x value in all then u will get 4,7,10,13,16.

So among them d least age is 4 i.e younger one.

Sudheer said: (Oct 24, 2011)  
Let x+(x-3)+(x-6)+(x-9)+(x-12)=50
5x-30=50
5x=80
x=16
is this correct or not?
if it is wrong then explain the reason..

Prince said: (Nov 16, 2011)  
For all who don't understand here is the simple explanation.

Let the last child ( 5th ) born be x years old,
3 years before the 4th child was born so his age has to be x+3,
now the 3rd child was born 3 years before the 4th child. so the age of 3rd child is 3+3 ie 6+x.
so on..we get
x ( last child ) + x+3 ( a child before x )+ x+6 + x+9 + x+12 =50.

so x+x+x+x+x + 3+6+9+12 =50
5x + 30 =50
5x = 50-30
5x = 20
x = 4.
where x is the youngest child.

Explanation in Hindi: :P
jo last baccha hua uski age x hai...jo usse 3 saal pehle paida hua hoga toh uski age to x se 3 saal badi ho hogi na...so x+3,
so usse 3 saal pehle hua hoga uski age x se 6 saal badi and so on.

Udhay Chandran said: (Jan 15, 2012)  
Lets assume that the first elder son age is X, then the difference in the age of 3 years among the consecutive child summing to the total age of 50 would be follow.Here (X-3) corresponds to 2nd elder child age and (X-6) corresponds to 3rd elder child age and so on

x+(x-3)+(x-6)+(x-9)+(x-12)=50 ----> (1)
5x-30=50
5x=80
x=16

The (x-12) in equation 1 corresponds to 5th child age and by substituting X = 16 & (X-12) = Y in equation 1 we ill get 5th child age as below

16 + 13 + 10 + 7 + Y = 50
46 + y =50
Y = 50-46
Y = 4

Mitali said: (Mar 31, 2012)  
I have a other way to solve it.
Avg of 50 = 50/5 = 10.
Hence, the middle No. In the series i.e. x+6=10 (middle no is the avg value of the series).
So x = 10-6= 4.

Em0 said: (Jun 2, 2012)  
I have an other way to solve it.

When 1st baby came and he became 3years old than other baby came. When 2nd baby became 3years old than 3rd baby came and 1st baby became 6years old like it 3x4 = 12, so 1st baby became 12 years old than 5th baby came 1st baby became 15 years old.

Like, 1st 15 2nd 12 3rd 9 4th 6 5th 3,

3+6+9+12+15=45 thair is 5 years. So give one year.

It will be.

4+7+10+13+16=50.

Siddhartha Roy Nandi said: (Jul 7, 2012)  
The Problem can be solved using Arithmetic Progression:

S = n/2{2a+(n-1)d}

a = youngest age(We have to calculate this)
n = Total no. of people(5)
d = Difference of Ages in the progression(3)
S = Summation of their ages(50)

Aarthi said: (Dec 3, 2012)  
X+12+x+9+x+6+x+3+x=50.

5x+30=50.

(x+6) =10.

X=4.

Sairam said: (Feb 9, 2013)  
(x+2),(x+4),(x+6),(x+8),(x+10).
Total: x+2+x+4+x+6+x+8+x+10 = 50.

5x+30=50
5x=20
x=4.

Drakshayani said: (Aug 26, 2013)  
x+ (x+3) + (x+6) + (x+9) + (x+12) =50.

Add all the x is 5x.

And all the numbers is 30.

Then,

5x+30 = 50.

5x = 50 - 30.

5x = 20.

x = 20/5.

x = 4.

So the age of the youngest child is 4.

Rgauri said: (Sep 19, 2013)  
Let us assume that:

a, b, c, d, e are five childs to him.

Let,

a = x;

b = x+3;

c = x+6;

d = x+9;

e = x+12;

Then,

x+(x+3)+(x+6)+(x+9)+(x+12) = 50;

Therefore,

5x = 20;

x = 4.

So,

a = 4.

Youngest one.

Sylivia said: (Nov 15, 2013)  
What is the age of the middle child?

Zeekut said: (Nov 17, 2013)  
x+3+x+6+x+9+x+12+x = 50.

5x+30 = 50.
5x = 50-30.

5x = 20.
x = 20/5.

x = 4.

Rohini said: (Nov 29, 2013)  
There are 5 children. Each is borned in 3 years gap.
It means age of childrens.

Let assume age of first children is x year.

Hence, age.

1st child is : x.
2nd : x+3.

3rd : x+6 i.e.(x+3+3) (simply 3rd child is born after 3 years from the birth of 2nd child).

Similarly,
4th child age : x+9.
5th child age is: x+12.

If we add all children age together.

x+ (x+3) + (x+6) + (x+9) + (x+12) = 50 (it is given in question The sum of ages of 5 children born at the intervals of 3 years each is 50 years. ).

By adding all x together and all numbers it comes.

5x + 30 = 50.
5x = 20(50-30).
x = 4(20/5).

Hence the age of all kids.

1st: x = 4 year.
2nd: x+3 = 4+3 = 7 year.
3rd: x+6 = 4+6 = 10 year.
4th: x+9 = 4+9 = 13 year.
5th: x+12 = 4+12 = 16 year.

Rags said: (Mar 6, 2014)  
Guys its very simple.

5 children s sum is 50;

So 50/5=10;

Will get 10 as the middle number, it means the age of 3rd child is 10yrs, so each child born 3 yrs diff, so 10 is middle means,

4 (+3yr gap) 7 (+3yr gap) 10 (middle child(+3yr gap)) 13 (+3yr gap) 16...

So youngest child age is 4.

Aswin Bhaskar said: (Mar 12, 2014)  
X, X+3, X+6, X+9, X+12=50
5X = 50-30.
5X = 20.
X = 4.

Priyanka said: (May 14, 2014)  
@Sylivia.

Look the options and add 3 to the 1st option and we can find it out i.e., 4+3=7.

Then 7+3=10 actually dat is de middle age: 10+3=13, 13+3=16.

Good luck.

Aravind said: (Jun 25, 2014)  
Here youngest means the smaller (4x), why we took x?

Rinshan said: (Jul 7, 2014)  
4x mean 4 times of the youngest ones age.

Mahesh said: (Jul 26, 2014)  
In the question its mentioned that "the intervals of 3 years each is 50 years" it means each child having 50 rit.

Ags said: (Aug 2, 2014)  
Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50

5x = 20
x = 4.

Age of the youngest child = x = 4 years.

Nikhil Goyal said: (Aug 14, 2014)  
Let the ages of children be (x-6), (x - 3), (x), (x + 3) and (x + 6) years.
Then, (x-6)+ (x-3)+ x + (x + 3) + (x + 6) = 50.

5x = 50,
x = 10.

Age of the youngest child = (x-6) = 4 years.

Suresh.Neelikonda said: (Jul 2, 2015)  
x+(x+3)+(x+6)+(x+9)+(x+12) = 50.
5x+30 = 50.
5x = 20.
x = 4.

Tina Rajput said: (Sep 13, 2015)  
The age of the youngest child should be x+12 and not x right?

x is the age of the oldest child.

Adittya said: (Nov 21, 2015)  
How can we get the age of the middle one or the oldest one?

Rupesh said: (Nov 28, 2015)  
Can any one, who has in depth knowledge in this can give the age of 3rd person?

Manish said: (Dec 18, 2015)  
Take the ages as x-6, x-3, x, x+3, x+6.

Now add all, (x-6)+(x-3)+(x)+(x+3)+(x+6) = 50.

All numbers will be cancelled and you will get:

5x = 50.
x = 10.

Youngest one will be x-6 = 10-6 = 4.

Basavaraj Marapur said: (Jan 20, 2016)  
Take youngest child = x.

So, (x-12) + (x-9) + (x-6) + (x-3) + x = 50.

5x-30 = 50;

5x = 20;

x = 4.

So youngest child is ---> 20;

Bhavya said: (Feb 9, 2016)  
We can take the youngest child as x.

Hence, 1st child = x.

2nd = x+3.
3rd = x+6.
4th = x+9.
5th = x+12.

Therefore, x + x + 3 + x + 6 + x + 9 + x + 12 = 50.

5x + 30 = 50.

5x = 50 - 30 (remember the sign changes when you transpose or change the side).

5x = 20.

x = 20/5 (remember the sign changes when you transpose or change the side).

x = 4.

So, the age of youngest child = 4 years.

Arun said: (Feb 26, 2016)  
Is there any short cut method please?

Ismail said: (May 23, 2016)  
If we consider the age of younger child x then after 3 years that child will (x + 3) again 3 years 2nd child born and he become (x + 6) like this up to date the child become (x + 12).

Then the age of younger brother should (x + 12) not only x.

Means answer should be (4 + 12). i.e =16.

Then why not getting 4 as the answer. Can anyone explain it?

Mathan said: (Jun 3, 2016)  
5x + (3 + 6 + 9 + 12) = 50.

5x + 30 = 50.
5x = 50 - 30.
5x = 20.

x = 4.

Prasanna said: (Aug 24, 2016)  
Average/total number.

A + B + C + D + E/5 = 50.
50/5 = 10.
C = 10.
10 - 3 = 7.

7 - 3 = 4 -> YOUNGEST ONE'S AGE IS 4yrs.

Nikhil said: (Oct 5, 2016)  
How we get x + 12?

Explain this step.

Lucky said: (Oct 6, 2016)  
@Nikil,

The sum of ages of 5 children and their difference is 3 years.

We consider that 1st children age be "x".

Then the second one be "x + 3".

3rd one be"x + 6".

4th one be "x + 9".

5th one be "x + 12" (because they all are born with three years difference).

Hema said: (Nov 9, 2016)  
Hi guys,

The best easy way to solve this type of question : You can go as per options and we can reduce the time consumption.

Go as per 1st option : for 1st child if 4 years then 2nd child 4+3 =7 years, Similarly 3rd child 10 years, 4th child 13 years and 5th child 16 years.
Then,
Add all the years if u get total 50 years (given in question) you decide your answer is correct. No need to calculate we can reduce our time for this type of easy question.

Saranya said: (Dec 30, 2016)  
Why are you taking odd ones?

Shawon said: (Mar 20, 2017)  
Can anybody solve the problem? Please.

Three times the present age of a father is equal to eight times the present of his son. Eight years hence the father will twice as old as his son at that time. What are their present age?

Ganesh Mudaliyar said: (May 13, 2017)  
There is a slight change they should have mention let the youngest child be x.

Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50,
5x = 20,
x = 4.

Age of the youngest child = x = 4 years.

Pooja said: (Jun 8, 2017)  
A man had three sons and they were born at an interval of five years. The sum of their ages after 5years will be 60 years. What was the age of youngest son five years ago?

Can anyone solve this?

Raquel said: (Jun 28, 2017)  
Step 1:Let x be the age of the youngest,
Step 2. Write out the equation,
x + (x+5) + (x+10)= 60,
Step 3: Isolate the variable x,
x+x+x+5+10=60,
3x+ 15 = 60,
3x= 60-15,
3x = 45,
x = 15 (present age of the youngest),

To find the age of the youngest five years ago we can use this expression ,
(x-5). Therefore, the age of the youngest five years ago is 10, since 15-5=10.

Suriya Khumar said: (Jul 3, 2017)  
HI guys.

First see the option.

In the question, they said that difference between the children is 3 years, and the total age is 50 years.

Hence,

Option A.

4+7+10+13+16 = 50 thats all.

Have a nice day!

Baby Jhie said: (Jul 28, 2017)  
Children age+interval 3
5 ---> x
4 ---> x+3
3 ---> (x+3+3)=x+6.
2 ---> (x+6+3)=x+9.
1 ---> (x+9+3)=x+12.

Sum of their age is 50.
x+x+3+x+6+x+9+x+12=50.
5x+30=50,
5x=50-30,
5x=20,
5x=20,
----------
5
x=4.

Let's check:

Eldest (1) (x+12)--4+12=16
Next (2) (x+9)--4+9=13
Third(3) (x+6)--4+6=10
Fourth(4) (x+3)--4+3=7
Youngest(5) (x)--4

Take note:
There is an interval of 3 years.

Karthika said: (Sep 12, 2017)  
Let the ages be,

X-6, x-3, x, x+3, x+6
5x=50
X=10
Youngest =10 - 6= 4.

Srini said: (Sep 24, 2017)  
Youngest child means x+12 is the youngest one rite?

Pramod ( Nepal) said: (Nov 1, 2017)  
@Pooja,

According to your Q 1st eq x+ (x+5) + (x+10) but if after 5 years.

The sum of there age 60 the new eq become (x-5) +x+ (x+5) = 60.

After solving x=20.

Youngest bro age is 15 but 5 years ago his age is 10.

Kanwal said: (Dec 16, 2017)  
How we get 5 in this?

Shyam Raj said: (Feb 27, 2018)  
How can we say that answer(4yrs) is the age of last younger one?

Malak said: (May 1, 2018)  
The sum of age of 3 sisters now is 25 years. If the oldest was born before the middle by 3 years and the middle was born before the youngest by two years. Find the age of each of them.

Please, anyone, answer it.

Akhil said: (Jul 12, 2018)  
According to me;

The youngest children age = x+12.
= 4+12.
= 16.

Vikram said: (Sep 23, 2018)  
Divide the sum of the ages by total no of children 50/5=10.
Now as we know that the age varies by 3 years...so take 10+3 &10-3=13&7.
then again take the age and sub and add 3. i.e; 13+3&7-3=16&4,
Now add all the operations 4 + 7 + 10 + 13 + 16 = 50.

Devakshi said: (Oct 7, 2018)  
x+(x+3)+(x+6)+(x+9)+(x+12)=50.
5x+30=50,
5x=50-30,
5x=20,
x=20/5,
x=4.
Ans=4.

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