Question

A two digits number is 4 times the sum of its digits and twice the product of the digits.find the number

Answer 1

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Assumption,

Tens digit be t

Also,

Ones digit be p

So,

Number = 10t + p

Situation,

10t + p = 4(p + t)

10t + p = 4p + 4t

3p - 6t = 0

p = 2t ................... (1)

10t + p = 2pt

Now,

Dividing both sides by pt,

10/p + 1/t = 2 .............. (2)

Now,

Substitute value of (1) in (2)

10/2t + 1/t = 2

5/t + 1/t = 2

6/t = 2

t = 6/2

t = 3

Now,

Substitute value of t in (1),

p = 2t

p = 2(3)

p = 6

Number = (10t + p)

= 10(3) + 6

= 36