Question

The sum of the ages oftwo friends is 20 years. Four years ago, the product of their ages is
ors was 48. Is the above situation possible? If so, determine their present ages.​

Answer 1

Answer:

Situation is not possible .

Step-by-step explanation:

Given-----> Sum of the ages of two friends is 20years , four years ago , the product of their ages was 48 .

To find ------> This situation is possible or not and if possible what are the present ages.

Solution-----> Let present ages of two freinds be x and y.

ATQ, Sum of present ages of friends = 20

=> x + y = 20

=> y = 20 - x

Four years ago ages of friends are ( x - 4 ) and

( y - 4 ) .

ATQ, four years ago , product of their ages = 48

=> ( x - 4 ) ( y - 4 ) = 48

=> ( x - 4 ) ( 20 - x - 4 ) = 48

=> ( x - 4 ) ( 16 - x ) = 48

=> 16x - x² - 64 + 4x = 48

=> - x² + 20x - 64 - 48 = 0

=> - x² + 20x - 112 = 0

Changing the sign of whole equation , we get,

=> x² - 20x + 112 = 0

Comparing this quadratic equation by

ax² + bx + c = 0 . we get,

a = 1 , b = - 20 , c = 112

b² - 4ac = ( -20 )² - 4 ( 1 ) ( 112 )

= 400 - 448

= - 48 < 0

So roots of quadratic equation is imaginary , so this situation is not possible .

Answer 2

AnswEr :

Let the Age of two friends be a and, b.

• Sum of Present Ages :

↠ a + b = 20 years

↠ a = (20 – b) years ⠀⠀—eq.( I )

$\rule{200}{2}$

$\underline{\bigstar\:\textsf{According to the Question Now :}}$

$:\implies\textsf{Product of Age 4 years ago = 48 years}\\\\\\:\implies\sf (a - 4)(b - 4) = 48\\\\\\:\implies\sf (20 - b - 4)(b - 4) = 48\qquad \dfrac{ \quad}{}from \:eq.(l)\\\\\\:\implies\sf (16 - b)(b - 4) = 48\\\\\\:\implies\sf 16b - 64 - {b}^{2} + 4b = 48\\\\\\:\implies\sf 20b - {b}^{2} = 48 + 64\\\\\\:\implies\sf 20b - {b}^{2} = 112\\\\\\:\implies\sf{b}^{2} - 20b + 112 = 0 \\\\\qquad\scriptsize{\bf{\dag}\:\texttt{Using Discriminat Formula Here :}}\\\\:\implies\sf Discriminat ={b}^{2} - 4ac\\\\\\:\implies\sf Discriminat ={( - 20)}^{2} - 4 \times 1 \times 112\\\\\\:\implies\sf Discriminat = 400 - 448\\\\\\:\implies\sf Discriminat = - 48\\\\\\:\implies\sf Discriminat = - 48 < 0$

⠀

∴ As Roots of this Equation is Imaginary, hence this situation isn't Possible.