### Brain Teasers

# Jack and Jill

Jack and Jill have grown up now, so much so that their ages add up to 64.

But Jill is confused as to how old each of them is. Jack gives her a clue: "I am 5 times as old as you were when I was as old as you are now."

Can you help Jill recall their ages correctly?

But Jill is confused as to how old each of them is. Jack gives her a clue: "I am 5 times as old as you were when I was as old as you are now."

Can you help Jill recall their ages correctly?

### Hint

Jack is much older than Jill than you might think...### Answer

Jack: 40 yrs. oldJill: 24 yrs. old

Explanation:

Let the present age of Jack be x and that of Jill be y. So, clearly, like everyone of you would have got: x+y=64.

The other equation is a bit tricky.

JACK JILL

y yrs. ?

(Their ages when Jack was the age that Jill is at present)

x yrs. y yrs.

(Their present ages)

Since we have moved back (x-y) yrs. to make Jack y yrs. old, to find the age of Jill at that time, we go back (x-y) yrs. from her present age. So, her age was y-(x-y) yrs. = 2y-x yrs.

Since Jack's present age is 5 times that age, x= 5(2y-x). Hence, we get the second equation.

Solving them, x=40 and y=24.

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