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Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit's age. After further 8 years, how many times would he be of Ronit's age?
Answer & Solution
Correct Answer:
Option
A
$$\eqalign{
& {\text{Let}}\,{\text{Ronit's}}\,{\text{present}}\,{\text{age}}\,{\text{be}}\,x\,{\text{years}}. \cr
& {\text{Then,}}\,{\text{father's}}\,{\text{present}}\,{\text{age}}\, \cr
& = \left( {x + 3x} \right)\,{\text{years}} \cr
& = 4x\,{\text{years}} \cr
& \therefore \left( {4x + 8} \right) = \frac{5}{2}\left( {x + 8} \right) \cr
& \Rightarrow 8x + 16 = 5x + 40 \cr
& \Rightarrow 3x = 24 \cr
& \Rightarrow x = 8 \cr
& {\text{Hence,}}\,{\text{required}}\,{\text{times}} \cr
& = \frac{{ {4x + 16} }}{{ {x + 16} }} \cr
& = \frac{{48}}{{24}} \cr
& = 2 \cr} $$
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Father is not three times of his son Ronit, Question given three times more than his son Ronit.
Let,
Ronit (Present) age = x
if Father is three times of his son Ronit
Then F =3x
But
Question says three times more than his son Ronit.
As, Ronit (Present) age = x
So Father age became F=(x+3x)
(Because father is more than his son Ronit, Not Three times of his son)
### Question Read carefully
Then father's present age is 3x
According to the question after 8years
(3x+8)=2.5(x+8)
3x-2.5x=20-8
.5x =12
5/10x=12
X=12×10/5
X=24
Ronit's present age 24
His father's present age
3x=3×24
=72
Again after 8years Ronit's age will be 24+8=32
Ronit father's age 72+8=80 which is 2.5 times than his son
Answer :option( B)
Let Rohit's Present age be R.
As given in the question (Father is aged three times more than his son Ronit).
So, The relation will become:
F=3R ----- (i)
After 8 years,
Father's Age= F+8
Rohit's Age= R+8
As given in the question (After 8 years, he would be two and a half times of Ronit's age.)
So, Now Relation will become:
(F+8)= 2.5*(R+8) ---- (ii)
Putting the value of F from Eqn. (i) in Eqn. (ii):
(3R+8)= 2.5*(R+8)
3R+8=2.5R+2.5*8
3R-2.5R=2.5*8-8
0.5R=8*(2.5-1)
0.5R=8*1.5
R=8*3
R=24
So putting the value of R=24 in Eqn (i), we get
F=3*24=72
According to the question(After further 8 years, how many times would he be of Ronit's age?):
So 8+8 years=16 years
Fathers age after 16 years= 88
Ronit's age after 16 years = 40
So, (Father's age/Son's age) = 88/40=2.2
Therefore fathers age is 2.2 times Ronit's age.
so 32+16/8+16= 2
here 16 years means 8 years +8 years
Ratio of father and Ronit's after 8 years= 5:2
So, difference of father's present age and age after 8 yrs = 5-4 = 1
Now 1 part = 8 yrs
Then father age 8 yrs hence = 8×5 = 40
And Ronit's age 8 yrs hence =8×2= 16
Their age after further 8 yrs = 48 and 24 respectively
I.e. father is 2 times of Ronit's age.
Father age is 3 time more than son age, not three times of son age. Kindly read question carefully
Plesae
que. says that Father is three time more then Ronit age so there equation should be F=3x;
please clarify fast because My Exam will be tomorrow Morning..
(4x+16) / (x+16) = (4*8 + 16) / (8 +16) = 48/24 = 2