Question

. Rohan's mother is 26 years older than him. The product of their ages after 3 years will
be 360 years. We need to find Rohan's present age.​

Answer 1

❍ Let the Rohan's present age be x and Rohan Mother's present age be (x + 26) respectively.

After three years their ages,

• Rohan's age = (x + 3)
• Rohan Mother's age = (x + 29)

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀

$\underline{\bigstar\:\boldsymbol{According\;to\;the\; Question\; :}}$⠀

⠀

• As it is given that, after three years the product of their ages (Rohan's age and Rohan Mother's present age) will be 360 years. Therefore,

$:\implies\sf (x + 3) (x + 29) = 360 \\\\\\:\implies\sf x^2 + 29x + 3x + 87 = 360 \\\\\\:\implies\sf x^2 + 32x + 87 = 360 \\\\\\:\implies\sf x^2 + 32x + 87 - 360 = 0\\\\\\:\implies\sf x^2 + 32x - 273 = 0\\\\\\:\implies\sf x^2 + 39x - 7x - 273 = 0\\\\\\:\implies\sf x(x + 39) - 7(x + 39) = 0\\\\\\:\implies\sf (x - 7) (x + 39) = 0\\\\\\:\implies\sf x - 7 = 0\;or\:x + 39 = 0 \\\\\\:\implies{\underline{\boxed{\frak{\purple{x = 7 \;or\:x =-39}}}}}\;\bigstar$

⠀⠀⠀

• By Ignoring negative value of x. Because age can't be negative. Therefore, taking x = 7.

⠀⠀⠀

Hence,

⠀⠀⠀

• Rohan's present age, x = 7 years.
• Rohan Mother's present age, (x + 26) = (7 + 26) = 33 years.

⠀⠀⠀

$\therefore{\underline{\textsf{Hence,\; Rohan's\: present\:age\:is\; \textbf{7 years}.}}}$

Answer 2

Answer:

Given :-

• Rohan's mother age is 26 years older than him. The product of their ages after 3 years will be 360 years.

To Find :-

• What is the present age of Rohan.

Solution :-

Let, the present age of Rohan be x years

And, the present age of Rohan's mother will be x + 26 years

$\longmapsto$ After 3 years ago :

Age of Rohan is x + 3 years

And, the age of Rohan's mother is x + 3 + 26 = x + 29 years

According to the question,

↦ $\sf (x + 3) (x + 29) =\: 360$

↦ $\sf x(x + 29) + 3(x + 29) =\: 360$

↦ $\sf {x}^{2} + 29x + 3x + 87 =\: 360$

↦ $\sf {x}^{2} + 32x + 87 =\: 360$

↦ $\sf {x}^{2} + 32x + 87 - 360 =\: 0$

↦ $\sf {x}^{2} + 32x - 273 =\: 0$

↦ $\sf {x}^{2} + (39 - 7)x - 273 =\: 0$

↦ $\sf {x}^{2} + 39x - 7x - 273 =\: 0$

↦ $\sf x(x + 39) - 7(x + 39) =\: 0$

↦ $\sf (x - 7) (x + 39) =\: 0$

↦ $\sf x - 7 =\: 0$

➠ $\sf\bold{\pink{x =\: 7}}$

Either,

↦ $\sf x + 39 =\: 0$

➠ $\sf\bold{\pink{x =\: - 39}}$

We can't take age as negative (- ve).

Then, x = 7.

Hence, the required present age of Rohan and Rohan's mother is :

✪ Present age of Rohan :

⇒ $\sf x\: years$

➦ $\sf\bold{\red{7\: years}}$

And,

✪ Present age of Rohan's mother :

⇒ $\sf x + 26\: years$

⇒ $\sf 7 + 26\: years$

➦ $\sf\bold{\red{33\: years}}$

$\therefore$ The present age of Rohan is 7 years.