sum of the present age of two friends are 23years 5 years ago product of their ages was 42 .find their ages 5 years hence
Answers
Answer:
5 years hence, one of them will be 16 years old and the other one will be 17 years old.
Step-by-step explanation:
Let the present age of the friends be 'x' and 'y' years respectively.
According to the condition in the question,
x + y = 23
x = 23 - y --- (i)
Five years ago, the ages of the friends would be 'x - 5' and 'y - 5' years respectively.
According to the condition in the question,
(x - 5) (y - 5) = 42 ---(ii)
Solving equation (i) and (ii) by substitution method.
Putting the value of x from equation (i) to equation (ii)
=> (23 - y - 5)(y - 5) = 42
=> (18 - y )(y - 5) = 42
=> 18y - 90 - y² + 5y = 42
=> 23y - y² = 132
=> y² - 23y + 132 = 0
=> y² - 11y - 12y + 132 = 0
=> y(y - 11) - 12(y - 11) = 0
=> (y - 11)(y -12) = 0
=> (y - 11) = 0 or (y -12) = 0
=> y = 11 or y = 12
if y = 11, then x = 12 (from equation (i))
if y = 12, then x = 11 (from equation (i))
These are their present ages.
The ages 5 years hence will be (x + 5) and (y + 5) years.
if x = 12 and y = 11 , their age 5 years hence will be 17 years and 16 years.
if x = 11 and y = 12 , their age 5 years hence will be 16 years and 17 years.
Therefore, 5 years hence, one of them will be 16 years old and the other one will be 17 years old.