Question

A two digit number is four times the sum and 3 times the product of its digits, find the number.

Answer 1

Let this two digit number be 'Xi. Which means X=10x (as it comes in tens digit). 

Then as per the question, 

XY = 4 (X + Y) 

⇒  4(X+Y) = 10 X+ Y ..... (i) 

and  XY= 3(XY)= 10X + Y ..... (ii) 

From (i), we get, 6X = 3Y

⇒ X = `"Y"/2`

Putting this in (ii) , we get : `(10 "Y")/2 + "Y" = (3 "Y")/2 xx "Y"`

`5"Y" + "Y" = 3/2 "Y"^2`

⇒ Solving this we get: 3Y²=12Y 

⇒ Y = 4

Hence X = `"Y"/2 = 2`

Hence , number is 24.