Question

7 year ago varun's age was five time the square of swati's age. 3 year hence, swati's age will be two-fifth of varun's age . Find their present age​

Answer 1

Answer:-

• Varun's age = 27years
• Swati's age = 9 years

Given:-

• 7 year ago Varun's age was five time the sqaure of Swati's age
• 3 year hence, Swati's age will be two-fifth of Varun's age

To find:-

• Present age of Varun and Swati= ..?

Find:-

Let Swati's age 7 years ago be x years.

Then, Varun's age 7 years ago =$5 {x}^{2}$

Swati's present age = (x+7)

Varun's present age = $5 {x}^{2} + 7$

Swati's age 3 year hence = (x+7+3)years = (x+10)years

Varun's age 3 year hence = $5 {x}^{2} + 7 + 3 = 5 {x}^{2} + 10years$

$(x + 10) = \frac{2}{5} (5 {x}^{2} + 10) \\ = > 5x + 50 = 10 {x}^{2} + 2 \\ = > \: 10 {x}^{2} - 5x - 30 = 0 \\ = > 2 {x}^{2} - x - 6 = 0 \\ = > 2 {x}^{2} - 4x + 3x - 6 = 0 \\ = > 2x(x - 2) + 3(x - 2) = 0 \\ = > (x - 2)(2x + 3) = 0 \\ = > x = 2 \: or \: x = \frac{ - 3}{2} \\ = > x = 2$

Hence, age cannot be negative

Swati's present age = (2+7)years =9 years

Varun's present age = $(5 \times {2}^{2} + 7)years = 27years$

Hope its help uh❤

Answer 2

$\huge\sf{ \underline{ \underline{Question}}}$

• 7 years ago varun's age was 5 times the square of swati's age 3 year hence Swati's age will be two-fifth of Varun's age. find their present age.

$\huge\sf{ \underline{ \underline{Answer}}}$

• $\sf{Swati\:age\:=\:9years}$

• $\sf{Varun\:age\:=\:27years}$

$\huge\sf{ \underline{ \underline{Solution}}}$

$\sf{Let\:age\:of\:swati\:=\:x+7}$

$\sf{\:\:\:\:\:age\:of\:varun\:=\:5\ x^{2}+7}$

$\sf{ \red{ \underline{ \underline{After\:3\:years}}}}$

$\mapsto\sf{\dfrac{2}{5}\times(5\ x^{2}+10)\:=\:x+10}$

${}$

$\mapsto\sf{2(5\ x^{2}+10)\:=\:5(x+10)}$

${}$

$\mapsto\sf{10\ x^{2}+20\:=\:5x+50}$

${}$

$\mapsto\sf{10\ x^{2}-5x+20-50\:=\:0}$

${}$

$\mapsto\sf{10\ x^{2}-5x-30\:=\:0}$

${}$

$\mapsto\sf{10\ x^{2}-20x+15x-30\:=\:0}$

${ }$

$\mapsto\sf{10x(x-2)+15(x-2)\:=\:0}$

${}$

$\mapsto\sf{(x-2)(10x+15)\:=\:0}$

${ }$

$\sf{x\:=\:2\:,\:\dfrac{-15}{10}}$

$\sf{ \blue{So\: present\:age\:of\: swati\:}}$

$\mapsto\sf{2+7\:=\:9years}$

$\sf{ \blue{So\: present\:age\:of\:Varun\:}}$

$\mapsto\sf{5\ (2)^{2}+7}$

$\mapsto\sf{20+7}$

$\mapsto\sf{27\: years}$