Discussion :: Problems on Ages - General Questions (Q.No.8)
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
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.
Dhanesh P G said: (Dec 5, 2019)
My solution is given by, The present sum of ages 60.
So 6 years ago the sum is 48.
Then the ratio is 5:1 it means 5x+x=6x=48.
Then x=8 and,
Age after 6 years is 40+12=52 and 8+12= 20.
Sushmitha C P said: (Jan 11, 2020)
Sum of both ages is F + S = 60 We can also write as F = 60 - S ------> Eqn 1. 6 years ago father age will be 5 times the age of son -> eq becomes F - 6 = 5 (S - 6)------> Eqn(2). Then substitute eq(1) to eq(2). Then eq becomes (60-S)-6 = 5 (S - 6). (60-S)-6 = 5S - 30, 60+30-6=5S+S, 84=6S, S = 14.
Then add 6 to it (because after 6 years so)so 14 + 6 = 20.
Srujan said: (Jan 31, 2020)
Thank you all.
Naximi said: (Apr 28, 2020)
Thanks @Amit.
Isha said: (Aug 23, 2020)
Very easy to understand, Thanks @Amit.
Nikhil G said: (Oct 16, 2020)
x+y = 60 -------------> eqn1
5x-6 = y-6 => 5x = y ----------> eqn2 Equating both equation:
y/5 = 60-y.
y=300-20y.
y=300/19.
y = 14 years.
After 6 years 14+6 = 20.
Abhi said: (Dec 15, 2020)
@Amit. You have already added 6 to bring question in present (x+6) & (5x+6). Now the outcome of this solution is 8yr right. This 8yr must be present age of son we have to add 6 to know future age hence, 8+6=14.
How have you added 8+6+6? I didn't understand please reply.
Hassan said: (Jan 4, 2021)
Very helpful. Thanks for explaining @Amit.
M Mahd Pakistan said: (Jan 9, 2021)
Thanks @Amit.
Rituparna Pati said: (Jun 13, 2021)
@Amit.
You have already added 6 to the years to convey the present years of both of them. Then why have you added another 6 years. I can't understand! Please explain it.
Mahendran Kamaraj said: (Dec 25, 2021)
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 years.
