Question

A two digit number is such that the product of its digits is 16 when 72 is added to the number the digits interchange their places. Find the number

Answer 1

Let'to be 10's digit=x
let to be 1'unit=y
A/q
xy=16
x=16/y
then,

10x+y+72=1oy+x
10x-x+y-10y=-72
9x-9y=-72
9(x-y)=-72
x-y=8
Now putting the value of x in another equation

y-x=8
y-16/y=8
y²-8y+16

y²-4y-4y+16
y(y-4)-4(y-4)
(y-4)(y-4)
y=4


Now putting the value of y in another equation,
x=16/y
x=16/4
x=4

now the required no
10x+y
10(4)+4
40+4
44

that's all

Sujeet