Aptitude - Problems on Ages - Discussion

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.

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.

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

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.

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?

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.

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.

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.

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?