# 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?

A. 2 times

B. $$2\frac{1}{2}\,{\text{times}}$$

C. $$2\frac{3}{4}\,{\text{times}}$$

D. 3 times

**Answer: Option A **

__Solution(By Examveda Team)__

$$\eqalign{
& {\text{Let}}\,{\text{Ronit's}}\,{\text{present}}\,{\text{age}}\,{\text{be}}\,x\,{\text{years}}. \cr
& {\text{Then,}}\,{\text{father's}}\,{\text{present}}\,{\text{age}}\, \cr
& = \left( {x + 3x} \right)\,{\text{years}} \cr
& = 4x\,{\text{years}} \cr
& \therefore \left( {4x + 8} \right) = \frac{5}{2}\left( {x + 8} \right) \cr
& \Rightarrow 8x + 16 = 5x + 40 \cr
& \Rightarrow 3x = 24 \cr
& \Rightarrow x = 8 \cr
& {\text{Hence,}}\,{\text{required}}\,{\text{times}} \cr
& = \frac{{ {4x + 16} }}{{ {x + 16} }} \cr
& = \frac{{48}}{{24}} \cr
& = 2 \cr} $$ ## Join The Discussion

## Comments ( 17 )

Related Questions on Problems on Ages

A. 2 times

B. $$2\frac{1}{2}\,{\text{times}}$$

C. $$2\frac{3}{4}\,{\text{times}}$$

D. 3 times

A. 4 years

B. 8 years

C. 10 years

D. None of these

A. 14 years

B. 19 years

C. 33 years

D. 38 years

Answer is 2.2 or 2 (1/5)

Question is clearly given that Father is aged three times more than his son Ronit.

Here,

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

Let Ronit's present age is x

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)

How 16 of 4x+16 comes

How 4x came

Let the Father's present age be F.

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.

from where do we get 4x+16 and x+16

after you found out the son's and his father's age 8 , 32 years, then you need to find their age ratio

so 32+16/8+16= 2

here 16 years means 8 years +8 years

Ratio of father and Ronit's present age = 4:1

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.

Hello Guys,

Father age is 3 time more than son age, not three times of son age. Kindly read question carefully

Answer is wrong.father age is 3 times ronit age ie 3x not x+3x

3times means 3x but how to 4x comes.. Ans is wrong

How to calculate the required ratio

Plesae

i am confused in Father=(x+3x);

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..

x = 8

(4x+16) / (x+16) = (4*8 + 16) / (8 +16) = 48/24 = 2

Can you please simplify the equation 4x+16/x+16

how to calculate required ratio and how it becomes 4x+16/x+16