Question

a two digit number is 5 times the sum of its digits and is also equal to 5 more than twice the product of its digit. find the number.

Answer 1

$\red\bigstar$QUESTION:-

⠀⠀⠀

•A two digit number is 5 times the sum of its digits and is also equal to 5 more than twice the product of its digit. Find the number.

⠀⠀⠀

$\orange\bigstar$SOLUTION:-

•Let the tens and units digit of the required number be x and y respectively. Then,

A/q

⠀⠀

• 10x+y=5(x+y) ⠀⇨ 4y=5x ⇨y=5x/4 ......(1)

⠀⠀

• 10x+y=2xy=5 ⠀⇨ 10x+5x/4 =2x×5x/4+5⠀[using (1)]

$\sf \implies \dfrac{45x}{4} = \dfrac{10 {x}^{2} }{4} + 5$

⠀⠀⠀

$\sf \implies10 {x}^{2} - 45x + 20 = 0$

⠀⠀⠀

$\sf \implies \sf2 {x}^{2} - 9x + 4 = 0$

⠀⠀⠀

$\sf \implies2 {x}^{2} - 8x - x + 4 = 0$

⠀⠀⠀

$\sf \implies2x(x - 4) - 1(x - 4) = 0$

⠀⠀⠀

$\sf \implies(x - 4)(2x - 1) = 0$

⠀⠀⠀

$\sf \implies x - 4 = 0 \: \: or \: \: 2x - 1 = 0$

⠀⠀⠀

$\sf \implies \: x =4 \: \: or \: \: x = \dfrac{1}{2}$

⠀⠀⠀

A digit cannot be a fraction

$\therefore \bf x = 4$

⠀⠀⠀

Putting x=4 in (1), we get:y=5

$\bf \therefore \: x = 4 \: and \: y = 5$

⠀⠀⠀

Hence,the required number is 45