Question

Aman is X years old now, Write his age 7 years from now and 7 years ago. Also, write the expression for his mother’s age who will be 3 times older than after 7 years.

Answer 1

Hint:-Here aman’s current age is given so for finding his age 7 years ago we have to subtract the no of years from his current age. And for finding the age 7 years from now we have to add the no of years with his current age. Because 7 years from now he will be 7 years older than the present age, So we have to add that.

Complete step-by-step answer:
As per given question, Aman’s Correct age is X years.
So, for finding the age 7 years ago, we have to subtract 7 from his current age, because 7 years ago he was 7 years younger than the present age, So, 7 years ago his age was (x-7) years and for finding the age 7 years from now we have to add, because 7 years from now he will be older 7 years more from his current age, So, 7 years from now his age will be, (x + 7) years.
$\therefore $ we consider his mother’s present age is ‘y’ years.
$\therefore $ After 7 years his mother's age will be ( y +7 ) years.
$\therefore $ Aman’s current age is x (according to question)
$\therefore $After 7 years Aman’s age will be (x +7) [$\therefore $ which is already elaborate 1st part of this problem]
According to question, After 7 years aman’s mother’s age will be 3 times of his (aman’s) age after 7 years,
So, $3\left( {x + 7} \right) = y + 7$
     $ \Rightarrow 3x + \left( {3 \times 7} \right) = 7 + y$
     $ \Rightarrow 3x + 21 = y + 7$
     $ \Rightarrow 3x + 21 - 7 = y$
     $ \Rightarrow y = 3x + 14$
So, Aman’s mother’s age is $\left( {3x + 14} \right)$, it is her present age.

Note: Here we have to notice the present age carefully and then for finding the previous age we just have to subtract that number of years and for finding the future age we have to add the years.
And for finding his mother’s age, when we write the equation we are multiplying 3 with Aman’s age which will be after 7years because his mother’s age is 3 times of his age (an age which will be 7 years from now).
So, equate his mother’s age with his. We are multiplying 3.