Question

the difference between two sister's age is 5 . 10 years ago if the elder one was twice as old as younger one .find their present age.

Answer 1

$\textbf {Question:}$

THE DIFFERENCE BETWEEN TWO SISTERS' AGES IS 5. 10 YEARS AGO, IF THE ELDER ONE WAS TWICE AS OLD AS YOUNGER ONE, THEN FIND THEIR PRESENT AGES.

Let's assume the sisters' ages as x and y respectively.

$\textbf {As per the question,}$

$x - y = 5 \\ y = x - 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: .......(i)$

$(x - 10) = 2(y - 10) \\ x - 10 = 2y - 20 \\ x - 2y = - 10 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: .......(ii)$

Substituting the value of y from (i) in (ii),

$x - 2(x - 5) = - 10 \\ x - 2x + 10 = - 10 \\ - x = - 20 \\ x = 20$

Substituting the value of x in (i),

$y = x - 5 \\ y = 20 - 5 \\ y = 15$
$\therefore \: their \: present \: ages \: are \: 20 \\ and \: 15 \: respectively.$

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