Aptitude - Problems on Ages - Discussion

Step 1:

Let us consider kunal age is = x and sager age is = y.

Six years ago ages of kunal and sager is = 6:5.

So we can write x-6/y-6 = 6/5--->A.

Next, four years hence ages of kunal and sager is = 11:10.

So we can write x+4/y+4 = 11/10--->B.

Step-2:

Solve equation A and B, so.

Eqn A becomes,

X-6/y-6 = 6/5, so cross multiply becomes.

5x-30 = 6y-36->5x-6y+6 = 0.

5x-6y = -6-->C.

Eqn B becomes,

X+4/y+4 = 11/10, so cross multiply becomes.

10x+40 = 11y+44-->10x-11y-4 = 0.

10x-11y = 4-->D.

Solve eqn C and D.

5x-6y = -6->C.

10x-11y = 4->D.

2xeqn c, we get.

10x-12y = -12->E.

10x-11y = 4->D.

Step 3:

Eqn E (-) eqn D, so we can get.

10x-12y = -12.

-10+11y = -4.

So -y = -16.

We know (-) is cancel, so y = 16 = sager age.

Really I feel my explanation will under stand you.

Guys, there is a shortcut for this method.

Let us take given options into consideration.

First, let's take option (a) that is 16 years (present age).

Given in the question that six years ago the ages of Kunal and Sagar is in the ratio (6:5) and we are asked to find the Sagar present age!

Hence 16-6 (six years ago) = 10.

10 is the multiple of 5 (Sagar age is 5x).

So condition one is satisfied.

In the next statement, they have given four years hence the ratio would be (11:10).

Meaning the Sagar's age is multiple of 10.

Hence (present age +four years).

We have taken option A into consideration that is 16.

So (16+4=20).

Which is a multiple of 10.

There you go both the conditions are satisfied and you have your answer.

6 years ago Kunal's age was 6x and 6 years ago Sagar's age was 5x.

The ratio 6 : 5 is given here for 6 years ago. Hence, we have to add 6 in the ratio (i.e., 6x + 6 and 5x + 6).

Note (Key point of the solution): If ratio should be given for present then we have to subtract 6 instead of add. But, the ratio is given here for 6 years ago.

Four years hence, Kunal's age will be 6x + 6 + 4 and Sagar's age will be 5x + 6 + 4.

Also, the ratio of their ages will be 11 : 10.

Then, 6x + 10/5x + 10 = 11/10

By solving this we get x = 2.

Hence, 6 years ago Sagar's age was 5x = 5x2 = 10 years and for the present, we have to add 6.

So, the present age of Sagar is 10 + 6 = 16 Years.

Hi to all, the solution to this question goes like this;

Let the present age of Kunal & Sagar be "X" & "Y".

For Six years ago, X-6/Y-6 = 6/5....situation (1).

For Four years hence, X+4/Y+4 = 11/10....situation (2).

From situation (1) we will calculate value of "X".

5X-30 = 6Y-36 (On cross multiplication).
5X = 6Y-36+30.
5X = 6Y-6 => x = 6Y-6/5....equation (i).

Now from situation (2), we substitute the value value of "X" in situation (2):

10x6Y-6/5 + 40 = 11Y+44.

Dividing denominator "10" by "5" in numerator we get.

2x6Y-6 + 40 = 11Y+44.
12Y-12+40 = 11Y+44.
12Y-11Y = 44+12-40.

Y = 56-40.
Y = 16.

Let present age of kunal and sagar is x and y. Now according to the question
six year ago the ratio of the ages of kunal and sagar was 6/5.

It means x-6/y-6=6/5. Now solve it and finally it is 5x-6y+6=0.....(1 equation).

Now four years after it means x+4/y+4=11/10. Now solve it and finally it is 10x -11y-4=0.....(2 equation).

Solve both equation 1 and 2. To solve firstly multiply the whole equation of 1 with 2 that is 10x-12y+12=0.

Now equate equation 1 and 2 that is 10x-11y-4=10x-12y+12. Finally y =16 which is the age of sagar at present.

I HOPE THIS SOLUTION WILL BE HELPFUL !

Let Kunal's present age = x and Sagar's present age = y.

6 years ago, Kunal's age:Sagar's age = (x-6):(y-6).

Now ATQ, (x-6):(y-6) = 6:5,solving which we get equation as:5x-6y = -6. Lets consider it as eq.1.

Now again, after 4 years, Ratio will be (x+4):(y+4) which is given as 11:10.
Solving which we get equation as 10x-11y=4. Let it be eq.2.

Therefore the 2 eq. are,
5x-6y=-6. Eq.1.
10x-11y=4. Eq.2.

Multiplying Eq. 1 by 2,it is 10x-12y=-12.Let it be eq. 3.
Subtracting Eq. 3 by Eq. 2,

10x-11y-10x+12y=16.
Therefore y=16, i.e Sagar's age is 16 years.

I hope you all will get this.

it is clearly said that on above question 6 years ago means 6 years back so we subtract 6 from original ages;

So x-6/y-6 =6/5,
5x-30=6y-36,
then we have 5x-6y=-6--> (1)
As like they said hence after that means add 4 years from present;
So x+4/y+4=11/10,
10x+40=11y+44,
then we have 10x-11y=-4--> (2)
From 1 and 2 we can solve,
2 ( 5x-6y=-6)
10x-11y=-4 we can subtract
....................................
-y = -16 so clearly y = 16 Ans.

1st step:

Six years ago, the ratio of the ages of Kunal & Sagar was 6 : 5 means 6x & 5x respectively i.e. 6x+6/5x+6 (added hear six because given "Six years ago").

2nd Step:.

Four years hence, means after 4 years, the ratio will be 11/10.

So we add hear 4 which mean.

(6x+6) +4/ (5x+6) +4 = 11/10.

6x+10/5x+10 = 11/10.

10 (6x+10) =11 (5x+10).

60x+100=55x+110.

60x-55x=110-100.

5x=10.

X=2.

3rd step:

Sagar's present age = 5x+6.

=5 (2) +6.

=16 years.

Hope you understand friends.

The explanation given according to the question was absolutely right and i came to this conclusion after scratching my head for an hour. It has the logic. I represent the same model of question here under, both follows the same pattern.

Q: Five years hence the ages of Ram and his Son will be in the ratio 5:2. Three years ago, the ratio of their ages was 7:2. Find the present age of his son.

This would help you in clearing the doubts of this brain eating question.

Thanks.

Let Kunal age be 'x' and Sagar age be 'y'.

6 years ago,
Kunal age is (x-6) years and Sagar age is (y-6) years and their ratio will be 6/5 (given).

x-6/y-6 =6/5 --eq 1.

According to second statement,

x+4/y+4 = 11/10 --eq 2.

Solving these two equations:

5x-30=6y-36 (eq3) and 10x+40=11y+44 (eq 4).

Solving eq 3 and 4 as.

10x+40=11y+44.
-2 (5x-30=6y-36).

------------------------.

10x+40=11y+44.
-10x+60=-12y+72.

------------------------.

100= -y+116.
y= 16 years.