Question

A two digit number is such that product of its digits is 20 .If 9 is added to the number the digits interchange their places .Find the number.

please answer as soon as possible ​

Answer 1

Answer:

Let two digit number is 10x+y,

where x and y are the two digits of number

As per question, xy=20.......(i)

and (10x+y)+9=(10y+x)

or 9x-9y+9=0

or x-y+1=0

or x-y = –1 .....(ii)

So (x-y)²=1

or x²+y²-2xy=1.....(iii)

putting the value of xy in above equation we get

x²+y²=41

So (x+y)²=x²+y²+2xy=41+40=81

so x+y=9......(iv)

Solving equation (ii) and (iv) we get

x=4 and y=5

So two digit number is

10x+y=40+5=45

If you satisfies on my answer then give me thanks