Question

sum of the present age of two friends are 23 year ,five year ago product of their ages was 42. find their ages 5 years hence​

Answer 1

Answer:

Their ages 5 year hence will be 16 and 17 years.

Step-by-step explanation:

Given :  

Consider the present age of friend A = x years

Consider the present age of friend B = y years

⇒ Sum of the present ages of two friends are 23 years.

so ,

x+y = 23

x=23-y------------ (i)

Five years ago age of the friend A was =(x-5) years

Five years ago age of the friend B was =(y-5) years

As per the problem, Five years ago product of their age were =42 years

$\therefore(x-5)\times(y-5)=42\\\\\Rightarrow(23-y-5)(y-5)=42\\\\\Rightarrow(18-y)(y-5)=42\\\\\Rightarrow(18y-90-y^{2}+5y)=42\\\\\Rightarrow(23y-90-y^{2})=42\\\\\Rightarrow(42-23y+90+y^{2})=0\\\\\Rightarrow(y^{2}-23y+132)=0\\\\\Rightarrow(y^{2}-12y-11y+132)=0\\\\\Rightarrow y(y-12)-11(y-12)=0\\\\\Rightarrow (y-12)(y-11)=0As (y-12)(y-11)=0$

therefore y=11 or y=12

If y=11 then x=23-y=23-11=12

If y=12 then x=23-y=23-12=11

Therefore the present age of the two friends are 11 years and 12 years

Therefore the age of the two friends after five years are (11+5)=16 years and (12+5)=17 years

Answer 2

Answer:

x+y=23

x-5×y-5=42

x=23-y

(23-y)(y-5)=42

23y-115-ysquare+5y=42

28y-y^2=157

y^2-28y+157

further solve it you will get answer

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