Aptitude - Problems on Ages - Discussion

6 years ago means 6yr back. So how can we add 6 in first step? (6x+6/5x+6).

Also why can't the age of sagar be 20 yrs at present, as we need to include 4 yrs from the question to get the age of sagar at present?

They have mentioned that 6 years ago the ratio will be 6x+6/5x+6=6:5 and taking present age as a reference after 4 years the ratio is 6x+6+4/5x+6+4=11:10 So the answer will be 16 years.

For some questions we are taking ago as + sign and some questions we are taking -sign could you please explain which sign we have to take? and why?

Let the present of kunal=x ,& sagar =y.

Given 6 years ago their ratio is 6:5, here 6 years should be subtracted from their present age.

i.e.,

1) (x-6)/(y-6) = 6/5 -----(1).

Given 4 years later means nothing but 2 years ago from their present age (or) again they come back 4 years from ago 6 years.

2) (x-2)/(y-2) = 11/10 -----(2).

Solving (1) & (2) we get sagar age y=10.

After 6 years sagar age is,

y+6 = 10+6 = 16.

Lets sons age x and father y.

Then,

x+y = 60.
x-6 = 5(60-x) (put y=60-x).

6x = 306.

x = 306/6.
x = 51.
Son will be 60-51 = 9.

9+6 = 15 years hence.

The word ago means before. So, we should subtract.

Hence, the equation should be.

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

Please, Explain me, if I am wrong.

Hi @Neha and @Faruk can you please explain what is "x" here?

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.

Hi @Satyajeet.

It'll be (6x+6)+4/(5x+6)+4 = 11/10 because before 6 years the ratio was 6:5 but here we are taking after 4 yrs of present i.e past of 6 yrs + 4yrs (from present).

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