Question

in two digit number is 4 times the sum and the three times the product of its digits find the numbers​

Answer 1

A two digit positive integer can be expressed as 10x+y, where x is the tens digit and y is the ones digit. For example, 37 = 3(10)+7.

So, 10x+y = 4(x+y) and 10x+y = 3xy

10x+y = 4x+4y

6x = 3y

y = 2x

Since y = 2x and 10x+y = 3xy, we have 10x+2x=3x(2x)

12x = 6x2 6x2-12x = 0

6x(x-2) = 0 x = 0 or x = 2

Since x can't be zero, x = 2

y = 2x = 4

The number is 24.

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Answer 2

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

Assumption,

Unit digit be p

Also,

Tens digit be t

Number = 10t + p

Situation,

⇒ 10t + p = 4(t + p)

⇒ 10t + p = 4t + 4p

⇒ 10t - 4t = 4p - p

⇒ 6t = 3p

⇒ 2t = p .................... (1)

We have,

10t + p = 3pt .............. (2)

Now,

From (1) we have,

⇒ 10t + 2t = 3(2t)t

⇒ 12t = 6t²

⇒ 6t² - 12t = 0

⇒ 6t(t - 2) = 0

⇒ t = 0, 2 (Value 0 is not applicable)

So,

Putting value of t in (1)

⇒ 2t = p

⇒ 2 × 2 = p

⇒ p = 4

Number

= 10t + p

= 10 × 2 + 4

= 24

Therefore,

Required number = 24