Aptitude - Problems on Ages - Discussion

8. 

The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:

[A]. 12 years
[B]. 14 years
[C]. 18 years
[D]. 20 years

Answer: Option D

Explanation:

Let the present ages of son and father be x and (60 -x) years respectively.

Then, (60 - x) - 6 = 5(x - 6)

54 - x = 5x - 30

6x = 84

x = 14.

Son's age after 6 years = (x+ 6) = 20 years..


Amit said: (Aug 17, 2010)  
We can also solve this as below:

Let six years ago son's age be x, and fathers age be 5x.

Then sum of their present age
(x+6)+(5x+6)=60
x+5x+12=60
6x+12=60
6x=60-12
6x=48
x=8

Hence six years ago son's age was 8 years
and present age is 8+6=14 years
Answer=after six years his age will be 14+6=20 years.

Sowmya said: (Sep 28, 2010)  
Thanks Amit.

Vijay said: (Oct 13, 2010)  
Thank you so nice and easy.

Shabana said: (Oct 30, 2010)  
We can also solve as..
x = son age
y = father's age
x+y=60 -----(1)
(y-6)=5(x-6)-----(2)
by solving (1)&(2) we get x=14 ,y=46
after 6 yrs son age = x+6
= 14+6=20

Shoeb said: (Dec 14, 2010)  
Thank for making this sum so simple....

Santosh said: (Dec 21, 2010)  
Hey amit you already added 6 initially,
(x+6)+(5x+6)=60
x+5x+12=60
6x+12=60
6x=60-12
6x=48
x=8 and at end we haveto add another 6 means 8+6=14 years ....then how it would be 20 so actual answer is also wrong

Parthi said: (Feb 11, 2011)  
Thank guys.

Sirisha said: (Feb 28, 2011)  
@santosh

Amit is right. He taking as ago, present, after.

Pankaj said: (Apr 30, 2011)  
Superb shabana keep it up.

Mrs Pallavi said: (May 19, 2011)  
Son's age= x, father's age is y.

x+y=60.........................(1)
as per 2nd statement
(y-6)=5(x-6)

5x-y=24........................(2)
therefore solving equ. 1 & 2
x=14 & y=46

3rd condition

Son age after 6 year
14+6= 20 year.

Jagadeesh said: (Aug 26, 2011)  
Thanks pallavi.

Rajinder said: (Sep 9, 2011)  
The sum of son and father's age can be written as
S+F=60 ----------(1)
before 6 years ago
5(S-6)=F-6
5S-30=F-6
5S-F=-6+30
5S-F=24 ----------(2)
ADDING (1) and (2),weget
6S=84
S=84/6=14
put s=14 in ist weget
F=46

Hence after 6 years Son;s age will be 14+6=20 years.

Priya said: (Sep 27, 2011)  
Let s be son and f be father.
s+f=60
this was 6 years ago there fore
(s+f)-6=60-6 . . .here f=5s therfore substut
s+5s-6=54 . . .6s=60
therefor s=10
aftr 6 years
s=16

Please tell wats wrong with my logic.

Manoj Verma said: (Dec 1, 2011)  
Suppose son's age=x father's age=y x+y=60 y-6=5(x-6) 60-x-6=5x-30 6x=84 x=14 after 6 years son's age=20

Appatakar said: (Dec 13, 2011)  
Awesome pallavi thanks.

Yakesh said: (Feb 15, 2012)  
Before(6 years back): 5x, x
Present:5x+6, x+6
After 6 years:5x+12,x+12
and 5x+6+x+6=60
x=8
after 6 years = x+12 = 8+12 = 20.

Venkatesh said: (Feb 29, 2012)  
A+B=60,--->1
6 yrs ago , (A-6)=(B-6)*5[bcz Six years ago, father's age was five times the age of the son]
A-6=5B-30,
A=5B-24, ----->2
By simplifying 1 and 2 we will get B=16.
Aft 6 yrs B+6=20.

Selvi.K said: (Apr 19, 2012)  
We will solve this problem by solving the two equation
Consider son's age=Y, Fathers age=X.
Let X+Y=60. (1)
6 years ago means
Son's age=X-6, Fathers age=Y-6.
So the equations changed as per the condition
5Y-6=X-6.
We get,
X-5Y=-24. (2).
Solve (1) , (2).
We get y=14, x=46.

After 6 years the son's age=14+6=20.

Kauthik said: (Aug 6, 2012)  
Father's age = x ; son's age = y

x+y = 60; x-6 = 5y; y+6 = ?

x = 5y+6

5y+6+y = 60

6y = 54

y = 9

Hence present age of son = y+6= 15.

I got answer like this. what's wrong in this method.

Chandana said: (Aug 20, 2012)  
I think so...
it's after 6 years,
in eqn x-6=5y u didnt reduced son's age to 6years(after 6years)
x-6=5(y-6)
then u get the answer..
x-6=5y-30
x=5y-24;

5y-24+y=60
6y=84
y=14

hence present age of son=y+6=20

Pandi said: (Aug 28, 2012)  
Now son age x and father age is y
then
x+y=60---->1
six years before son=x-6, father=5(x-6)
so
y-6=5(x-6)
y-6=5x-30
5x-y=24--->2
solve 1 and
get x=14
x is present age
after six years x+6=20

Rohan Magar said: (Aug 31, 2012)  
@Amit thanks yar. Your method is easy and simple to understand :).

Muhammad Umair Kabir said: (Sep 20, 2012)  
Let 'F' be the Father's Age and 'S' be the Son's Age.

According to situation:

F+S = 60 EQ ---- 1
F-6 = 5(S-6) ,
Which is F-6 = 5S-30 EQ ---- 2

F = 5S -24 EQ ---- 3
Put this in EQ 1

5S - 24 + S = 60
6S = 84
S = 14

After 6 Years Sons age will be S = 14 + 6 = 20

Nil_Dhongde@Yahoo.Com said: (Oct 15, 2012)  
s=x
f=y
x+y=60......................(1)
6 years ago
(y-6)=5(x-6)
i.e
y-6=5x-30
Therefore at present age we have
y-6+6=5x-30+6
i.e
y=5x-24

From (1)
x+5x-24=60
6x=84
x=14

Therefore after 6 yrs sons age will be
14+6=20

Vijay Anand said: (Aug 23, 2013)  
@Priya.

Your logic is correct but you have to subtract 12 from 60. You have subtracted 6 for sons age and for fathers age you have to subtract another 6 know so it will be 60-12 = 48 not 54.

If you want me to explain precisely means please let me know.

Sunil said: (Mar 30, 2014)  
Fathers age 4 times of his son means.

Sons age X.
Fathers age 4x.

Or

Sons age 4x.
Fathers age x.

Which one is right ? How to solve explain ?

Nandhini said: (Apr 4, 2014)  
@Sunil.

Case I is right.
Logically father's age should be more than son's age.
So 4x is greater than x so its right to take son's age x and father's age 4x.


Case-II is logically wrong.
Let x=20 i.e father's age then
Son's age will be 80 i.e 4x.
How could a 20yrs father can have 80 yrs son.

Hence case - I is right sons age x and fathers age 4x.

Ashok said: (Sep 15, 2014)  
Take father age = x.
Son age = y.

Sum of father+son = 60.
x+y = 60 eq(i).

6 yrs ago father age is 5 times the age of son.

x-6 = 5(y-6).
x-6 = 5y-30.
x = 5y-30+6.
x = 5y-24.

Sub x value in eq(i).
5y-24+y = 60.
6y = 60+24 = 84.
y = 14.

Then 6 yrs after the son age = 14+6 = 20 years.

Imran Ali Korai said: (Oct 15, 2014)  
Present age of son = x.
Present age of father = 5x.

6 years ago.

Son's age = x + 6.
Father's age = 5x + 6.

Sum of their ages.

X+6+5x+6 = 60.
6x = 48.
X = 8.

Son's age = x+6 = 14.

After Six Year's
14+6 = 20.

Hence 20 is correct answer.

Sudha said: (Dec 11, 2014)  
We can solve like this also:

Father is mentioned as 'f'.
Son is mentioned as 's'.

Sum of father and son age ==> f+s = 60 ----- (1).

Before 6 years ==> (f-6) = 5(s-6).

F-5s = -24 -------------- (2).

Solve equation 1 and 2 we can get the value of s = 14.

The current age of son is ===> 14.
After 6 year ==> 14+6 = 20.

Avinash said: (Oct 4, 2015)  
In previous sum + for ago in this this sum your using - for ago what we have to use say properly.

Somya Khare said: (Oct 11, 2015)  
Son = x.
Father = y.

Then, x+y = 60.....(1).

6 years ago.

(y-6) = 5(x-6).

That is y-6 = 5x-30.

Therefore at present age we have y-6+6 = 5x-30+6.

That is, y = 5x-24.

From (1).

x+5x-24 = 60.
6x = 84.
x = 14.

Therefore after 6 years sons age will be.

14+6 = 20.

Divya said: (Dec 8, 2015)  
I'm confused with this answer. I solve like this correct me if I'm wrong.

Let the present age of father = x.

Let the present age of son = y.

Sum of present age: x+y= 60 then equate will become: y = 60-x.

6 years ago the age of father will be 5 times the age of his son.

Father: x-6.
Son: y-6.

Equate these 2 equation, would become:

x-6 = 5(y-6).
x-6 = 5y-30.

By substituting the value y = 60-x:

x-6 = 5(60-x)-30.

x = 46 (present age of father).

Substitute the age of father to y = 60-x would gives us the present age of his son.

y = 60-46.

y = 14 (present age his son).

14 is my answer;

Thank you!

Zulminan Ahmed said: (Jan 5, 2016)  
Let father's age = X.

Let son's age = Y.

So, A/Q X+Y = 60 (Equation 1).

But six years ago father's age was five times the age of the son.

So, X-6 = 5(Y-6) (Equation 2).

Now putting the value of X = 60-Y from (Equation 1) in (Equation 2).

So, 60-Y-6 = 5(Y-6).

So the value of Y = 14.

But in question we have to find the son's age after 6 years so added 6 in 14. So, answer will be 20 years.

FINE!

Kirti said: (Jan 26, 2016)  
Father age = f, son age = s.

Then f+s = 60;

f+6 = 5(s+6).

On solving s = 6;

Then present age of son = s+6 = 6+6 = 12;

Then after 6 years it will be = 12+6 = 18;

What is wrong in that?

Siva said: (Feb 1, 2016)  
6 years ago son age = x, then father = 5x.

Present age of son means x+6 like that father age is 5x+6.

x+6+5x+6 = 60. So x = 8, here it is.

After 6 years son age will be x+6+6 = 8+6+6 = 20.

Dhinu said: (Sep 6, 2016)  
Let the present age of the father is F, Son's present age is S.

The sum of their ages S + F = 60.

Fathers age 6 years ago (means - 6) F - 6,

Sons age 6 years ago S - 6,

Now given Six years ago, father's age was five times the age of the son.

Six years ago, father's age: F - 6 = 5(S - 6),

F - 6 = 5(S - 6) ---> Eq1

F + S = 60 ---> Eq2

by solving we get S = 14.

Question is to find after(ADD) 6 years so ADD 6.

Hence, Sons's age after six years will be 20 years.

Nish said: (Oct 24, 2016)  
Age of the son 6 years ago = 'X'.
Age of the father 6 years ago = '5X'.

At present sum of the father and son's age = (X + 6) + (5X + 6) = 60.
=> X = 8 which is assumed as the age of 6 years ago so, at present age of the son is X + 6 i.e 8 + 6 = 14.

After 6 years age of the son will be = 14 + 6 = 20 years.

Sindhu Kalyan said: (Nov 5, 2016)  
Thank you @AMIT.

Pravin Garodi said: (Nov 13, 2016)  
Consider son present age is X and father present age is Y.

X + Y = 60 consider this is first equation,

6 year ago father age is,
(Y - 6) = 5(X - 6),
5(X - 6) = Y - 6,
5X - Y = 24 this is second equation.

After solving 1 and 2 equation,
X = 14,
After 6 year son age is 14 + 6 = 20.

Koteswararao Chimmili said: (Nov 28, 2016)  
Sum of present ages of a father and his son is 60 years.
Son + Father = 60

Six years ago:

Son + father = 60 - 12( six years ago means son-6 and father-6 )
Son + father = 48 -------->equation 1.

Father's age was five times the age of the son.
Son age x;
Father age 5x;
x = 5x.
Son age and father age substitute in equation 1.
Son + father = 48.
x + 5x = 48.
6x = 48.
x = 8 (x = 5x).

The present age of son:
Six years ago the age of son+6.
8 + 6 = 14.

After 6 years, son's age will be:
Son present age +6.
14 + 6 = 20.

Bharath said: (Dec 28, 2016)  
@All.

Let father & son's age be x&y.

As said present sum of x + y = 60.

& six yrs ago father's age was five times the age of his son i. e
(x-6) = 5(y-6)>>>eq 1.

x + y = 60>>we can ryt this as x = 60 - y.
So, substitute x value in eq 1.

(60 - y - 6) = 5(y - 6)
54 - y = 5y - 30
54 + 30 = 5y + y
84 = 6y.
So,
y = 84/6 = 14,
y = 14.
And y's age after 6 yrs =(y + 6).
= 14 + 6 = 20yrs.
So answer is D

Akash said: (Feb 28, 2017)  
6 years ago their age ratio was 5x : x right?

Then to find thier present age add 6yeras to both of them,
Now it becomes 5x+6 : x+6.
A/c data sum of their present age is equal to 60.
Now. 5x+6(father's age) + x+6(son's age) =60.
i.e 5x+6+x+6 = 60,
6x+12 = 60,
6x = 48,
x = 8.

x is son's age six years ago;
Son's present age is 8 + 6 =14.
Son's age after 6years from present is 14+6 = 20.

Shaila said: (Apr 17, 2017)  
Thank you everyone for explaining the solution.

Akshay said: (Jun 3, 2017)  
Simple Steps:

The Sum of Father and Son age: F+S=60.
Before 6 years condition: F-6=5(S-6); F=5S-24,
Put F in F+S=60 i.e,
5S-24+S=60 ; S=14

After Six years, S=14+6 = 20.

G.Bharath Reddy said: (Sep 16, 2017)  
Simple steps:

Let the ages of father and be y,x;
x+y+6=60;
Before 6 years,fathers age was x+6=5x+6
x+6+5x+6=60;
6x+12=60;
6x=48;
x=8;
So,son age is 8yrs;
At that moment,son age is=8+6=14yrs;
After 6yrs=14+6;
20 yrs/.

Haider said: (Sep 19, 2017)  
We can solve it by this method.

The sum of the ages =60
six years ago
we will subtract 12 years, 6 year each,
then sum would be 48.
divide by 6, bco s they are in the ratio of 1:5.
8 : 40 would be the answer,
Add 12 years to 8 and we get 20.

Alekhya said: (Nov 9, 2017)  
Father = 60-x.
6 years ago so (-) symbol if it is after 6 years means we add (+) symbol.

We add 6 to both sides,
(60-x)-6 = (x-6).

Here ques asked father's age was five times the age of the son

So,
(60-x)-6 = five times of(x-6) /(x-6) is sons age)/.
(60-x)-6 = 5(x-6).
54-x = 5x-30.
6x = 84.
x = 84/6.
x = 14.

After 6 years, son's age will be:
Son age x.
After six years so;
x+6.
14+6 = /20 years/.

Anil said: (Dec 30, 2017)  
Present age of F+S=60.
F=60-S.
6 years ago age of F+S=60-6-6=48-----(1)
and 6years ago son age is (s-6) and father age is 5(s-6).
Substitute these are in eq(1).
5(s-6)+(s-6)=48,
5s-6s+s-6=48,
Present age of son is S=14.
From F=60-s,
=>F=60-14,
Present age of father F=46.

After 6years son age is S=14+6
S=20 years.
After 6 years father age is F =46+6=52.

Vikas said: (Dec 30, 2017)  
Let the ratio of father and son 6 years ago was 5x:x.
Both father and son age's sum 6 years ago was,
60-12=48,
Then, 5x+x=48,
6x=48,
x=8.
Father age was 5*8=40 and son's age was 8.
At present father age is 40+6=46 and son's age is 8+6=14.
At present father and son's age some 46+14=60.
Then how the son's age is 20?

Rass said: (Apr 3, 2018)  
The age of A and B three years ago were 'x' and 'y+2' years, therefore the sum of their ages 4 years hence will be?

Can someone solve this?

Vidyaram Meena said: (Aug 30, 2018)  
There is another way to solve the same problem.

Let's suppose son age y and father age x.
according to question
x+y=60 ----> eqn(1).
and
x-6=5(y-6).
x-5y=-24----> equ(2).

By solving eqn(1) and eqn(2) we get y=14.
From question.

Then, y+6=14+6=20.
Hence after 6 years, the age of son is 20.

Gaurav Kumar said: (Apr 17, 2019)  
Thank you so much for explaining the answer.

Prithiv Raj said: (Jul 6, 2019)  
Let father age be x.
Son be y.

X+y=60,
X-6=5y,
Y=x-6/5.

Sub y in above eq.
X+x-6/5=60.
5x+x-6=300.
6x=294.
X=49 father age.
Sub x in above.
49+y=60.
Y=11.
After 6 years 11+6=17 years.

Teena Joy P J said: (Jul 30, 2019)  
Here, in this question, we can see 3 periods of time(past, present, future).
Take past first, ie, 6 yrs b4:

son=X and dad=5X.

Now take present:

Son=X+6 and Dad=5X+6.

Given a hint that at present their sum of ages is 60; a task made easy.

X + 6 + 5X + 6 = 60,
X = 8.

Now take future (we have to find ans in future):

After 6 more yrs:
Son=X+12 and dad=5X+12
So the son will be 8+12 yrs old.

The age of son =20.

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