Question

The product of age of ramu 5 years ago and his age 9 years after is 15. Determine present age of ramu

Answer 1

let Ramu's age be x

ramu's age before 5 years = x - 5

ramu's age after 9 years = x + 9

( x - 5 ) ( x + 9 ) = 15

x2 + 4x - 45 = 15

x2 + 4x - 45 - 15 = 0

x2 + 4x - 60 = 0

sum = 4 , product = -60

x2 + 10x - 6x - 60 = 0

x ( x + 10 ) -6 ( x + 10 ) = 0

( x - 6 ) ( x + 10 ) = 0

x = -10 , 6

age cannot be negative

so present age of ramu = x = 6

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.

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

The product of these ages is 15.

NOW,

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

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

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

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