Question

If now Kate is 3 times as old as Jan, and 6 years ago she was 6 times older than Jan, how old are they both now?

Answer 1

Answer:

acc to question

3x- x= 6x+6

2x= 6x +6

6x-2x= 6

4x=6

x= 6/4= 3/2

Answer 2

Let us take Jan's age which is now or present as x( taking it as a reference or helping hand for our question)

If now Kate is 3 times as old as Jan,then her present age will be 3x(3 times Jan's age)

Now according to the question,

The question is saying about 6 years ago.

So 6 years ago Jan's age was (x-6)years and Kate's age was (3x-6)years.[The question said 6 years ago so we subtracted 6 from their present ages.]

So if it says 6 years ago,she(Kate) was 6 times older than Jan.

So if Jan's age was (x-6) and Kate's age was (3x-6) ,six years ago respectively and Kate was 6 times older than Jan ,it literally means that if Jan's age was 1 unit then Kate's age would be 6 times of Jan's age which is 6 units.

JAN'S AGE•(1 unit)

KATE'S AGE•••••• (6 units) [•represents a unit]

This implies

6(3x-6)=(x-6)

18x-36=x-6

18x-x=-6+36

17x=30

x=30/17.

so if present ages were x and 3x respectively then

Jan's age =x =30/17 years.

Kate's age=3x=3*30/17=90/17 years.