Question

Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age

Answer 1

EXPLANATION.

To find rohan present age.

rohan mother is 26 years older than him.

=> Let the age of rohan be = x

=> Let the age of his mother be = ( x + 26 )

The product of age 3 years from now,

=> Rohan age will be = ( x + 3 )

=> age of his mother be = ( x + 26 + 3 )

=> ( x + 29 )

Their products of their age 3 years from

now = 360.

=> ( x + 3 ) ( x + 29 ) = 360

=> x² + 29x + 3x + 87 = 360

=> x² + 32x = 273

=> x² + 32x - 273 = 0

=> x² + 39x - 7x - 273 = 0

=> x ( x + 39 ) - 7 ( x + 39 ) = 0

=> ( x - 7 ) ( x + 39 ) = 0

=> x = 7 and x = - 39

=> x ≠ -39

=> x = 7

Therefore,

Age of rohan = x = 7 years

Age of rohan mother = x + 26 = 7 + 26 = 33 yrs

Answer 2

$\bf{\underline{\underline{Question:-}}}$

Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.

$\bf{\underline{\underline{Solution:-}}}$

Let,

• The age of rohan be X
• Age of rohan's mother is x + 26

$\bf{\underline{\underline{After\:Three\: years\:ago:-}}}$

Thier age will be

• x + 3 and x + 29

$\bf{\underline{\underline{According\:To\: Question:-}}}$

$\sf :→ (x+3)(x+29)=360 \\ \sf :→ x^2+(3+29)x+87=360 \\ \sf :→ x^2+3x+29x+87=360 \\ \sf :→ x^2+32x+87-360=0 \\ \bf ★\: By\: Splitting\: Method \\ \sf :→ x^2+32x-273=0 \\ \sf :→ x^2+39x-7x -273=0 \\ \sf :→ x ( x+39)-7(x+39)=0 \\ \sf :→ (x-7)(x+39)=0 \\ \sf :→ (x-7)=0 , (x+39)=0 \\ \sf :→ x=7 , x = -39$

We neglected x = -39

$\bf{\underline{\underline{Hence:-}}}$

• Rohan's age = x = 7 years
• Rohan's mother age = x + 26 = 7 + 26 = 32years