Aptitude - Problems on Ages - Discussion

5. 

Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?

[A]. 24
[B]. 27
[C]. 40
[D]. Cannot be determined
[E]. None of these

Answer: Option A

Explanation:

Let the present ages of Sameer and Anand be 5x years and 4x years respectively.

Then, 5x + 3 = 11
4x + 3 9

9(5x + 3) = 11(4x + 3)

45x + 27 = 44x + 33

45x - 44x = 33 - 27

x = 6.

Anand's present age = 4x = 24 years.


M.Pradeepa said: (Jan 28, 2011)  
Why the number 3 is added to 5x and 4x?

Srinivasan said: (Feb 3, 2011)  
Three years hence, the ratio of their ages will become 11 : 9 respectively.

So we need to add 3 on both side.

Gangadhararao said: (Feb 9, 2011)  
5 children, youngest 3yrs old and no 2 children have the same age, sum of their age is 26. Find the age of eldest.

Give me explanation.

Vijay said: (Feb 21, 2011)  
In the answer column they put 24 as the answer, please answer to my doubt if anand current age is 24 (as specified) then 3 years later his age will be 21 then how will you specify the age 21 in 5:4. Can divide the age 21 by 4 ?

Ravi said: (Apr 21, 2011)  
Give solution for 11/9.

Vandhanasuberwal said: (May 7, 2011)  
Ratio of the age of two persons is given. Let their age be in the ratio 5x &4x. it becomes 5x/4x .then in the question it is given,3years hence{means after 3years} then add 3in 5x/4x then we get 5x+3/4x+3.but in the question it is given that after 3years the ratio becomes 11\9 .SO IT becomes as 5x+3/4x+3=11/9. Now we can solve the question...

Ramakhanna said: (May 11, 2011)  
Three years hence ======> three years from present age.

The dictionary meaning for the word "hence" is "FROM NOW".

I think this will be useful in calculations.

Payal said: (May 21, 2011)  
Three year hence means AFTER THREE YEAR.

So, WE ADD 3 YEAR OK GUYS.

Shyam Kumar said: (Aug 16, 2011)  
Could any explain why should we multiply 4x.

Varun said: (Aug 28, 2011)  
Can any one tell me that how 4x has occured.

Rk333 said: (Aug 29, 2011)  
Here Sameer age & Anand age are assigned to x.

How is it possible? why we can't take two variables?

Kishan said: (Sep 17, 2011)  
Can any one tell me how to read 4x and 5x. In both value we can assign same variable? Is it possible?

Srini said: (Nov 4, 2011)  
Can some one give short cut to solve this ?

Murugan K said: (Dec 14, 2011)  
5 years ago A age was 3 times as old as B . If A is 30years older than B .The present age of A?

Agila said: (Jan 5, 2012)  
Given Ratio 5:4----->(1)
Difference between the ratio is 1
After three years 11:9---->(2)
Difference between the ratio is 2
Both the ratio difference are not same.

So muliply (1) by 2, we get 10:8
||ly multiply (2) by 1, we get 11:9. now the difference are same
Anand's present age=8*3=24 years

Vinothini said: (Feb 4, 2012)  
I hope my solution will help you...

Now Sameer age be x, Anand be y.

Ratio is x/y = 5/4 fine.... then 3 years after right, so x+3/y+3 = 11/9,

Then, will produce the eqn...4x=5y--------->1

9x+27=11y+33---------->2

We obtain that is x=5y/4, put into eqn 2,

9*5y/4-11y=33-27
45y-44y=6*4

y = 24 so simple friends.

Sameer said: (Mar 23, 2012)  
@vinothini good method.

Sajid said: (Jul 14, 2012)  
Remember @agila the ratio are not for a period.

Swathy said: (Feb 6, 2013)  
Ratio after 3 yrs ,

5x+3 11
----- = --
4x+3 9

9(5x+3)=11(4x+3)
45x+27 = 44x+33
45x-44x+27=33
x+27=33
x=6.

Present age of anand=4*6 = 24.

Iti said: (Jun 10, 2013)  
The total ages of the a, b and c 80 years. What was the total of their ages three year ago ?

Sriteja said: (Jun 13, 2013)  
Hai @Iti the problem can be solved as,

a+b+c=80 then after 3 years (a+3)+(b+3)+(c+3)=80+9=89

The given problem can be solved in other method as,

Given x/y=5/4;
After 3 years (x+3)/(y+3)=11/9;
Solving 9x-11y-6=0;
4x-5y=0;

We get x=30 y=24 Hence answer is 24 years.

Kaustubh said: (Jun 14, 2013)  
How did 5x+3/4x+3 = 11/9.

Siva said: (Aug 10, 2013)  
@Agila.

Given Ratio 5:4----->(1).
Difference between the ratio is 1.
After three years 11:9---->(2).
Difference between the ratio is 2.
Both the ratio difference are not same.

So multiply (1) by 2, we get 10:8.
||ly multiply (2) by 1, we get 11:9. now the difference are same.
Anand's present age=8*3=24 year.

How here 8 will be please tell me?

Vijay Anand C said: (Aug 17, 2013)  
@Iti and @Sriteja.

Hi friends since they have asked as 3 years ago we have to subtract it and not add.

A+B+C = 80,

Before 3 years or 3 years ago means,

A-3.
B-3.
C-3.

80-9 = 71.

So b4 3 years A+B+C = 71.

Vijay Anand C said: (Aug 17, 2013)  
@Murugan k.

QUE--> 5 years ago A age was 3 times as old as B . If A is 30years older than B .The present age of A?

Answer--> Before 5 years A=3B.

So after 5 years A's age increases by 5 so does the B's age. We get
A+5 = 3B+5-----------(eqn1)(this is present because I have increased 5yr from past).

A is 30 year older than B so A=B+30--------(eqn2),

Since we have to find the value of A we convert(eqn2)cas B=A-30--------(eqn3).

Now substitute (eqn3)in(eqn1).

A+5 = 3(A-30)+5.

A = 3A-90.

2A = 90.

A = 45 and B = 15.

Samuel Gbeneka said: (Sep 10, 2013)  
It can also be solved using formula : bt(c - d)/ (ad - bc).

Where a = 5, b = 4, c = 11 and d = 9.

t = 3.

4* 3(11 - 9)/(5*9 - 4*11)= 12* 2/ 45- 44.

= 24/1= 24. So the answer is 24.

Magesh said: (Sep 16, 2013)  
The respective ratio of the present age of A and B is 8:9. The sum of their ages is 68. What will be the respective ratio of their ages 10 years hence?

Anand said: (Oct 22, 2013)  
2013(present age) = 5 : 4
2016(3 years hence) = 11:9

5x+3/4x+3 = 11/9.

Doing cross multiplication. You'll get value x=6.
We need to sent Anand's present age.

Anand's ratio = 4x.
4*6 = 24.
That the answer.

Vinitha said: (Feb 17, 2014)  
@Samuel.

How can we use this formula bt(c-d)/(ad-bc)?

Pratik said: (Jun 4, 2014)  
x = ((11-9)*3)/(9*5-11*4).
So x = 6.

So Anand present age = 4*x = 24.

Raj said: (Jun 14, 2014)  
I think here is an error in answer,

If anand present age is 24(as 4 * 6 = 24, sameer age would be 5 * 6 = 30), here as mentioned in the question the ratio of their present age should be 11/9, but here the ratio according to the ans would be 30/24=5/4(5:4)(as per present age).

But we need to get 11/9 as the ration.

Anands present age would be 4x + 3 = 4*6+3=24+3 = 27.
And Sameer present age would be 5x + 3 = 5*6+3 = 33.
Then the ratio will satisfy, as 33/27 = 11/9(11:9 present ratio).

Can anyone justify existing answer.

Jyoti Bala said: (Jun 20, 2014)  
Why we take x for both?. May we take 2 different variables. I m not getting really.

Aarti Dike said: (Oct 13, 2014)  
3(11-9)/5*9-11*4 = 6.

Sameer and Anand present ratio is 5:4.

6*4 = 24.

Sai said: (Nov 29, 2014)  
Given ratios :

5:4 and 11:9 now.
3x2 (difference of 11:9)/45-44(5*9-4*11).
= 6x4 = 24 .

Krishna Chaudhary said: (Jun 4, 2015)  
@Vijay.

I think there is mistake in your solution.

According to me a = 50 and b = 20.

As the first equation can also be written as a-5 = 3(b-5).

To make it present 5 is subtracted both sides.

Pavan Nayak said: (Aug 31, 2015)  
I think 27 is answer. Because, When you take present ratio as 11:9, Sameer age will be 33 and Anand age will be 27 (multiplied by 3). When you go back 3 years.

Their age will be 30 and 24 (divided by 6). So, it will be of ratio 5:4. which is correct ratio as given data. Explain if I am wrong.

Surya said: (Jan 14, 2016)  
All explanations are good but some errors are present.

Irene said: (Feb 6, 2016)  
Please help me, I still don't understand. How we got 11/9?

Inna Reddy Chilakala said: (Feb 12, 2016)  
Anand present age:

4*(11-9)*3/5*9-11*4 = 4*2*3/1 = 24.

J K Reddy said: (Feb 25, 2016)  
Dear all nice answer thank you.

Renea said: (Apr 14, 2016)  
Hi, please explain the second step of the solution.

In this part of the equation 45x + 27 = 44x + 33. How +27 and + 33 came?

Aman Verma said: (Jun 15, 2016)  
First, write the present ages of Sameer and Anand as 5 and 4 respectively.

Now after three years their ages are 11 and 9 respectively.

Now to find the age of Anand. You have to multiply the present age of Anand.

i.e. (4 * 3(11 - 9)) / (11 * 4 - 9 * 5).

You will get the requires age of Anand, where 3 is times of the year, 11 and 9 are the ages of Sameer and Anand after 3 years.

Dileep Goli said: (Sep 7, 2016)  
Let the present ages of Sameer and Anand be X and Y.

Also given in question x and y are in the ratio 5 : 4 then, X/Y = 5/4 ---> eq [1]
After 3 years hence(later) & their ratios are = x + 3/y + 3 = 11 : 9.
9(x + 3) = 11(y + 3),
9x + 27 = 11y + 33,

9x - 11y = 6---> eq[2].
Ffrom eq [1], x = 5y/4 --> eq [3].
Substitute eq [3] in eq [2].

9(5y/4) - 11y = 6,
45y - 44y = 24,
1y = 24,
Then, y = 24. the present age of Anand(y) is 24.

Shyamala said: (Nov 11, 2016)  
I agree with @Agila.

Rahul said: (Nov 28, 2016)  
The ratio of A's age 3 years ago and B's age 5 years ago is 4 : 5. If A is 4 years younger than B then what is B's Present age?

Please tell me the solution.

Vamshi said: (Apr 13, 2017)  
Why not 11x/9x?

Rajshri Dubey said: (May 5, 2017)  
The ages of Nelson and Michael are in the ratio 3:5. After 9 years, the ratio of their ages will become 3:4. What is the present age of Michael?

Please explain this.

Phataleakshaykumar said: (May 30, 2017)  
Let Nelson present age =3x and Michael present age =5x, After 9 years, so adding
(3x+9)/(5x+9) = (3/4).
x = 3.
m = 5x.
m = 5(3) = 15.

Srinath said: (May 31, 2017)  
One year ago Ganguly and Sachin ages are in the ratio 6:7.4 years hence, the ratio of their ages will become 7:8. How old is Sachin?

Please give me the answer.

Vivek said: (Jun 23, 2017)  
Thanks for the given explanation.

Siddharth said: (Jun 30, 2017)  
@Srinath.

Let present ages of Ganguly and Sachin be x & y respectively.
Product of extremes = Product of means.
6(y-1)=7(x-1) &.
7(y+4)=8(x+4).
x= 31 and y= 36.

Jaison said: (Jul 10, 2017)  
SHORTCUT METHOD.

Since they are asking ANAND's present age the ratio for Anands present age is 4.
So check the options which go for 4 table.
24 goes for 4 so 24 is the answer.
Suppose the ask Anand's age 3 years later the ratio is 9 so 3 years later his age will be 27 since 27 is divisible by 9.

Aman Chawla said: (Jul 18, 2017)  
Calculation can be reduced by using components and dividend which is applied on ratio's on both sides of equals.

Here is the method -> num1/den1 = num2=den2.
-> APPLYING COMPONENDO AND DIVIDENDO ON BOTH SIDES.
-> (num1+den1)/(num1-den1) = (num2+den2)/(num2-den2).

So here it goes,
(5x + 3) / (4x +3) = 11/9,
using above method it reduces to below in one go,
(9x + 6) / x = 10,
=> x = 6.

The requires answer then would be 4*x (using given ratio) is 24(answer).

Deepthi said: (Aug 16, 2017)  
Can we do like this?

5x+3=11x
4x+3=9x
===>
20x+15=45x
20x+12=44x
===>
3=x

Is this right?

Satish said: (Aug 22, 2017)  
Let me explain this in a simple procedure. The First ratio is 5:4.
We have to find Anand age after 3yrs.
Second ratio 11:9
So add 3 to both the numbers.y we r adding 3 is in question they gave after 3yrs
So the new ratio is 14:12

First ratio is 5:4.
New ratio is 14:12.
In this Anand age ratio is 4 AND 12.

Now check the option which is exactly divisible by both the numbers and that's the answer.

Sonu said: (Aug 31, 2017)  
The ratio between presents ages of Pand Q is 3:4 respectively. If Q, s present age is 20 years, what will be the ratio of ages after 5 years?

Can anyone solve this?

Vinay Biranje said: (Sep 20, 2017)  
Sameer and Anand age ratio is 5:4.

After 3 years.

Sameer and Anand age ration is 11:9.
The diffrence between presnet and after age is 6 & 5.
After cross multiplying to the difference of ratios samerr age 5x = 5*5 = 25.
Anand age 4x =6*4 = 24.

That's it.

Junaid said: (Dec 29, 2017)  
Let me make it simple for you guys.

First, solve make ratios then equation:
5:4, which is 5x for Sameer and 4x for Anand : 5x/4x.

Three years from now 5x+3/4x+3 =11/9, solving this equation you get x=4.
How put 4 back on x places which is 5(4)/4(4)= 30/24 you get,

Hence 30/24 divide by 6 you get 5/4 further if u add 3 years from now, which 33/27, divide it by 3 you get ratio of 11/9.

Ajay said: (May 18, 2018)  
Four years back Sham's age was 3/4th of Ram's age that time. Four years from now, Sham's age would be 5/6th of Ram's age that time. What is Sham's age today?

Can anyone solve this?

Pandian Thanikodi said: (May 21, 2018)  
@All.

Please tell me that how possible the age ration will change on years? if both are in 5/4 ratio means after three years they should be in 5/4 only, how possible to become 11/9.

Rahul Deb said: (Jul 11, 2018)  
The ratio of the present age of a and b is 7:4 after 2 years their ages will be in the ratio of 5:3 what will be the ratio of A's age after 5 years to B's age now?

Can anyone solve this?

Sadiq said: (Jul 27, 2018)  
Why does 4x multiply by x = 6?

Kplakshmi said: (Aug 4, 2018)  
@ Sonu.

The ratio means short answer of fraction eg: 20/25 short answer is 4/5 so we can write in the form of 4x/5x.

~ the fraction of numerator and denominators are divided by the same number that's called x
P/Q=3x/4x(presentratio) Q's present age is 20.
4x =20 ; => x= 5.
after 5 years, (3x+5/4x+5) = 20/25.
Then the ratio is 4/5.

Deepanshu said: (Oct 1, 2018)  
The ratio of their present age is 5:4.
After 3 years, the ratio become 11:9.

Now, the difference is not equal which is 6:5 this ratio should be equal whenever to ask such a question. When equal their ratio new ratio is;
10:8
And 11:9.
Then; 1=3.
And asked is 8*3=24.

Hariprasad K N said: (Mar 27, 2019)  
Here 5:4 is taken with x variable 5X/4X but why the ratio after 3 years 11:9 is not taken with variable x as 11X/9X. Please clarify.

Kumar said: (Jun 28, 2019)  
According to me, it is X=6.

Why multiply by 4(5:4)?

When the current ratio leads to multiplying by 9 (11:9), where they have asked to find the present age of Anand after 3years.

Shaik Hashma said: (Aug 11, 2019)  
Here, the present ratio is 5: 4, 5x:4x then after 3years means 5x+3/4x+3equalto 11/9 if we cross multiply this we got X value is 6 then substitute in 4x then 4*6 then 24.

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