Aptitude - Problems on Ages - Discussion

6 years ago means we have to subtract as per the formula. Then why did they add in this problem?

Here consider There current ages x and y.
So according to 1 st condition.
X-6/y-6=6/5 --------> (1)

And according to 2 and Condition
X+4/y+4=11/10 --------> (2)

Solving (1) and (2) we get
10x-11y=4 --------> cross multiplication of (1)
5x-6y=-6 --------> cross multiplication of (2)
10x-11y=4 --------> (3)

So multiplying -2 (5x-6y=-6) we get;
-10x+12y=12 --------> (4).

Solving equations (3) and (4) we get;
y =16.
That is Sagar age.

How to add 4? please explain the step in detail.

It is 6 years ago, then how you guys added it? kindly read it.

(x-6)/(y-6)=6/5 ---> i
(x+4)/(y+4)=11/10 ---> ii
By solving i and ii , we get y=16.

Anwser is E.

Because the given ratio not verified.
let present age 16 years after five years 21 (16+5).
21 not multiple of 10.
and also 16 not multiple of 5.

False answer because ago indicate minus and hence or later indicate plus.

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.

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.

In this question, why we add 4 to both numerator and denominator?