Question

rohan mother is 26 years older than him the product of their ages (in years) 3 years from now will be 360 .find the Roman S present age​

Answer 1

Answer:

Step-by-step explanation:

Let Rohan's age to be x

His mother's age to be y

According to question

y=x+26......(1)

Also 3 years from now ,product of their ages will be 360

So,

(x+3)(y+3)=360

Putting value of y

(x+3)(x+26+3)=360

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

x^2+29x+3x+87=360

x^2+32x+87-360=0

x^2+32x-273

x^2+39x-7x-273

x(x+39)-7(x+39)

(x-7)(x+39)

x=7,-39

Age can't be in negative

So, Rohan's age is 7 year

His mother's age is (use EQ1)

y=x+26

y=7+26

32 year

Answer 2

❍ 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)

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

⠀

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.

$Therefore,</p><p>\begin{gathered}:\implies\sf (x + 3) (x + 29) = 360 \\\\\\:\implies\sf x^2 + 29x + 3x + 87 = 360 \\\\\\:\implies\sf x^2 + 32x + 87 = 360 \\\\\\:\implies\sf x^2 + 32x + 87 - 360 = 0\\\\\\:\implies\sf x^2 + 32x - 273 = 0\\\\\\:\implies\sf x^2 + 39x - 7x - 273 = 0\\\\\\:\implies\sf x(x + 39) - 7(x + 39) = 0\\\\\\:\implies\sf (x - 7) (x + 39) = 0\\\\\\:\implies\sf x - 7 = 0\;or\:x + 39 = 0 \\\\\\:\implies{\underline{\boxed{\frak{\purple{x = 7 \;or\:x =-39}}}}}\;\bigstar\end{gathered}$

⠀⠀⠀

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

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Hence,

Rohan's present age, x = 7 years.

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

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