Question

The product of Shikha’s age five years ago and her age 8 years later is 30, her age at both times being given in years. Find her present age.

Answer 1

Answer:

Let the present age of Shikha be ‘a’ years.

Given, product of Shikha’s age five years ago and her age 8 years later is 30

 

⇒ (a – 5)(a + 8) = 30

⇒ a2 + 3a – 40 – 30 = 0

⇒ a2 + 10a – 7a – 70 = 0

⇒ a(a + 10) – 7(a + 10) = 0

⇒ (a – 7)(a + 10) = 0

⇒ a = 7 years

Answer 2

$\bf{\large{\boxed{\sf{\red{Answer:}}}}}$

Present age of Sikha is 7 years.

$\bf{\large{\sf{\green{Explaination:}}}}$

Given :-

• Product of Shikha's age five ago and her age 8 years later is 30.

To find :-

• Present age of Sikha

Solution :-

Let the present age of Sikha be x years.

Her age 5 years ago = (x - 5) years

Her age 8 years later = (x + 8)years

As per the question,

$\implies$ $\bf{(x-5)}$$\bf{(x+8)}$ = 30

$\implies$ $\bf{x ( x + 8)}{-5(x+8)}$ = 30

$\implies$ $\bf{x^2+8x}{-5x\:-\:40}$ = 30

$\implies$ $\bf{x^2}{+\:3x\:-\:40}$ = 30

$\implies$ $\bf{x^2}{\:+\:3x\:-\:40\:-30\:}$ = 0

$\implies$$\bf{x^2\:+\:3x\:-\:70}$ = 0

$\implies$$\bf{x^2+ 10x - 7x - 70}$ = 0

$\implies$$\bf{x\:(x\:+10)\:-\:7\:(x+10}$ = 0

$\implies$ $\bf{(x+10)\:(x-7)\:=\:0}$

$\implies$$\bf{x+10\:=\:0\:\:OR\:\:x\:-7\:=0}$

$\implies$$\bf{x\:=\:-\:10\:\:OR\:\:\:x\:=\:7}$

x = - 10 is not acceptable since age cannot be negative.

•°• Shikha's present age = 7 years.