Question

The product of ramus age five years ago and his age 9 years later is 15. find ramus present age

Answer 1

Let Ramu's present age be X years, then his age 5 years ago will be (x - 5) years and his age 9 years from now will be (x + 9) years.

now, A/Q ( according to the question)
(x - 5) × (x + 9) = 15
so, x(x + 9) - 5( x +9) = 15
x^2 + 9x - 5x - 45 = 15
x^2 + 4x - 45 = 15
by transposing 15 to left side
x^2 + 4x - 45 -15 = 0
x^2 + 4x - 60 = 0
by using splitting the middle term method

x^2 + 10x - 6x - 60 = 0
x ( x + 10 ) - 6 ( x + 10 ) = 0
(x + 10) (x - 6) = 0
therefore,
( x + 10 ) = 0 × ( x - 6 )
(x + 10 ) = 0
so, x = -10

similarly, (x - 6) = 0
x = 6

now we know that age cannot be in negative so, the negative value of x i.e -10 will get rejected and x = 6 would be the present age of Ramu.

Answer 2

$\huge{\text{\underline{QUESTION}}}$

The product of Ramu's age (in years) five years ago with his age (in years) 9 years later is 15. Find Ramu's present age.

$\huge{\text{\underline{SOLUTION}}}$

Let Ramu's present age be x years.

Then, His age 5 years ago = ( x - 5 ) years.

His age 9 years ago = ( x + 9 ) years.

_____________________________

$\textsf{\underline{Given }} -$

The product of these ages is 15.

NOW,

$. ^{.} . \: \: (x - 5)(x + 9) = 15 \\ \\ = > {x}^{2} + 9x - 5x - 45 = 15 \\ \\ = > {x}^{2} + 4x - 45 - 15 = 0 \\ \\ = > {x}^{2} + 4x - 60 = 0 \\ \\ = > {x}^{2} + (10 - 6)x - 60 = 0 \\ \\ = > {x}^{2} + 10x - 6x - 60 = 0 \\ \\ = > x(x + 10) - 6(x + 10) = 0 \\ \\ = > (x + 10)(x - 6) = 0$

____________________________

$x + 10 = 0 \\ = > x = - 10$

$x - 6 = 0 \\ = > x = 6$

And we know that x will not be negative

So, x ≠ -10

x = 6

__________________________

Hence, Ramu's present age is 6 years.

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$\huge{\text{\underline{THANKS}}}$