Question

A two digit number is three times the product of its digits and four times the sum of the digits. Find the number.

Answer 1

Say two digit number is $ab$ then

$ab=10a+b$

According to the given conditions-

$3\times a\times b=10a+b$ ...... (1)

And

$4(a+b)=10a+b$

$4a+4b=10a+b$

$3b=6a$

$b=2a$ substituting in equation (1), we get

$6a^2-12a=0$

$6a(a-2)=0$

So, $a=2$ and $b=4$

Hence, the number is $24.$