Question

the sum of Ages of a son and his father is 55 years and the product of their ages is 600 find their ages​

Answer 1

Answer:

Let the father's age be x

Let the son's age be y

According to question

x+y=55...........(1)

xy =600..........(2)

${(x - y)}^{2} = {(x + y)}^{2} - 4xy \\ {(x - y)}^{2} = {55}^{2} - 4 \times 600 \\ (x - y) = \sqrt{625} = 25.......(3)$

Solve equation 1 and 3

x + y=55

x - y =25

2x = 80

x = 40 years

y =15 years

Answer 2

Let Age of Son=x years

Let Age of Father= y years

Sum of Their Age is 55 years

X+Y=55 years

X=55-y (Equation 1)

Product of Their Age=600

X×Y=600

Substituting Value of x as 55-y

(55-y)y=600

55y-y²=600

-y²+55y-600=0

0=-(-y²+55y-600)

0=y²-55y+600

By Middle Term Spilliting

y²-15y-40y+600=0

y(y-15)-40(y-15)=0

(y-40)(y-15)=0

So Now

Y-40=0

Y=40

Y-15=0

Y=15

X+Y=55

X+15=55

X=55-15

X=40

X+Y=55

X+40=55

X=55-40

X=15

X is Age of Son and It Can't be 40 years means More than Father age y=15

So Y=40

Father Age is Y=40 years

Son Age is X=15 years

Father=40 years

Son=15 years