Aptitude - Problems on Ages - Discussion

@Any where ago means you have to subtract but here given mistake. If I am wrong then please explain me?

Want to know if 6 years ago ratio of age is taken as 6x and 5x.

Then at last why ratio of age is taken only 11 and 10 in equation.

Its the ratio of age so should be taken as 11x and 10x.

Let the ages of kunal and sagar be x and y years respectively.

Then,(x-6)/(y-6) = 6/5.

=>x = (6y-6)/5.

Similarly; (x+4)/(y+4) = 11/10.

=>(6y-6+20)/(5y+20) = 11/10.

=>60y+140 = 55y+220.

=>5y = 80.

=>y = 16 years.

Therefore, sagar present age is 16 years.

Why we have added 6 years instead of deducting as it is given that 6 years ago?

6 years ago itself the ages are 6x, 5x respectively. Then hence 6 years it becomes 6x+6, 5x+6 right?

Six years ago means we have to deduct 6 from the current age but from the present age to after 4 years, they mentioned the ratio so.

From past 6 years we have to add 6 to come to present age and from present age we have to add 4. So total it will become like (x+6) i.e. is present and plus 4 i.e future.

So we get (x+6+4). Thats it.

(m-6) = (n-6)(6/5) --> 1.
(m+4) = (n+4)(11/10) --> 2.

Equating, 'm' we get,
(n-6)(6/5) + 6 = (n+4)(11/10) - 4.

Then n = 16 = Sagar's age.

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 !

These questions with their answers will play the crucial role to my ability.

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.