Question

the ages of two persons differ by 16 years if 6 years ago the elder one be three times as old as the younger one find their present ages​

Answer 1

$\huge\sf{\underline{\underline{Answer:}}}$

$\large\rm{\underline{\star{Given:-}}}$

The ages of two persons differ by 16 years and 6 years ago, the elder one is three times as old as the younger one.

$\large\rm{\underline{\star{To\:find:-}}}$

The present ages of both persons.

$\large\rm{\underline{\star{Solution:-}}}$

Let the age of elder and the younger person be x and y years respectively.

Then,

According to the question-

$\large\sf{\implies x = y + 16.........(i) }$

6 years ago-

$\large\sf{Elder\:person's\:age= (x-6) years. }$

$\large\sf{Younger\:person's\:age=\:(y-6) years}$

$\large\sf{But \:according\: to \:the \:question-}$

$\large\sf{\implies (x-6) = 3 (y -6) }$

$\large\sf{On\:using\:equation\:(i) -}$

$\large\sf{\implies y + 16 - 6 = 3 (y -6) }$

$\large\sf{\implies y + 10 = 3y - 18}$

$\large\sf{\implies 3y - y = 10 + 18}$

$\large\sf{\implies 2y = 28}$

$\large\sf{\implies y = \frac{28}{2}}$

$\large\sf{\implies y = 14\:years}$

Put y = 14 in equation (i) -

$\large\sf{\implies\:x = (14 + 16)\:years}$

$\large\sf{\implies x = 30\: years}$

Hence, the ages of elder and younger person is 30 years and 14 years respectively.

Answer 2

Answer :

The present ages of younger one and elder one are 14 years and 30 years respectively.

Explanation :

Given : Ages of two persons differ by 16 years. If 6 years ago the elder one will be three times as older as the younger one.

To find : Present ages of them.

Soultion :

Let the age of elder one be x years

Let the age of the younger one be y years

Difference of age between them = 16 years

=> x - y = 16

x = 16 + y ------- eq(1)

6 years ago:

The age of elder one = (x - 6) years

The age of younger one = (y - 6) years

According to the question:

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

16 + y - 6 = 3(y - 6)

10 + y = 3y - 18

3y - y = 10 + 18

2y = 28

y = 28/2

y = 14

Subtitute y = 14 in eq(1)

x = 16 + 14

x = 30

So the present ages of younger one and elder one are 14 years and 30 years respectively.