Aptitude - Problems on Ages - Discussion

Lets take Kunal and Sagar's age as x & y.

6 years ago, x-6/y-6 = 6/5 --> 5x-6y+6 = 0 -> A.

4 years hence, x+4/y+4 +11/10 --> 10x-11y-4 = 0 ->B.

Solve A & B,

y(Sagars age) = 16.

Let the 6 years ago ages was 6s & 5x;

Now at present; its ration is (6x+6)/(5x+5);

By next statement; 4 years hence; the age rations will become as; (6x+6+4)/(5x+6+4) = 11/10.

By its values x = 2;

Now as sagar's present age is = 5x+6 = 5*2+6 = 16 year;

Simple!

Let present ages of kunal and sagar be k and s respectively.

Then 6 years ago (k-6)/(s-6) = 5/6.

After 4 years (k+10/s+10) = 11/10.

After solving I got sagars age as 8 years. What wrong in this? Please help me.

As per concept you provided in ago we go for subtraction then how here addition of 6 done. Really I got confuse please help me.

Do it like this,

Let present age of Sagar & Kunal be "x" & "y".

Then, x-6/y-6 = 6/5....equation (1).

Similarly, x+4/y+4 = 11/10....equation (2).

From equation (1) on cross multiplication we get,

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

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

Substituting the value of "x" in equation....(2) we get.

10*(6y-6/5)+40 = 11y+44.

2*(6y-6)+40 = 11y+44.

12y-12+40 = 11y+44.

12y-11y = 44+12-40.

y = 16.

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.

In 6 years ago means -6 is comes why you have to use +6 in this equation?

@Faruk explained clearly, see it @Bhuvana.

Here we are calculating the present of Sagar, so instead of subtraction they used addition.

Six years ago : x-6/y-6 = 5/6.

5x-30 = 6y-36.

5x-6y = -6-----equation 1.

Four years after: x+4/y+4 = 11/10.

10x-11y = 11y+44.

10x-11y = 4------equation 2.

By solving equations 1 and 2 we get y = 16.

Why we add 6 years instead of subtracting in some cases if we got 6 we are subtracting why in this we are adding 6?