Question

The sum of ages of a girl and her sister is 32 yrs and product of their ages in
yrs is 252. Find their present ages.​

Answer 1

ANSWER:-

LET THE AGE OF GIRL BE X AND THE AGE OF HER SISTER BE Y

GIVEN:- X+Y = 32

WHERE AS :- X×Y= 252

SO ; LET X BE 14

AND LET Y BE 18

SO X+Y= 14+18

= 32

SO X×Y=18×14

252

THEREFORE THE AGE OF GIRL IS 14 AND OF HER SISTER IS 18.

Answer 2

Let ,

The present age of girl and her sister be x and y

By the given condition ,

$\star$x + y = 32 or x = 32 - y ------ (i)

$\star$xy = 252 ---------------- (ii)

Put the value of x = 32 - y in eq (ii)

$\sf \implies (32 - y)y =252 \\ \\ \sf \implies</p><p>32y - {y}^{2} = 252 \\ \\ \sf \implies</p><p> {y}^{2} - 32y + 252 = 0 \\ \\ \sf \implies </p><p> {y}^{2} - 18y - 14y + 252 = 0 \\ \\ \sf \implies</p><p>y(y - 18) - 14(y - 18) = 0 \\ \\ \sf \implies</p><p>(y - 14)(y - 18) \\ \\ \sf \implies</p><p>y = 14 \: and \: y = 18 </p><p>$

Put the value of y = 14 in eq (ii)

$\sf \implies x(14) = 252 \\ \\\sf \implies x = \frac{252}{14} \\ \\\sf \implies x = 18$

Again , Put the another value of y = 18 in eq (ii)

$\sf \implies x(18) = 252 \\ \\\sf \implies x = \frac{252}{18} \\ \\\sf \implies x = 14$

$\therefore$Girl's age = 18 yrs or 14 yrs and Girl's sister age = 14 yrs or 18 yrs