Question

Four times the sum of the digits of a
two-digit number is 18 less than the number
and is also 9 less than the number formed by
reversing its digits. find the product of its
digits.​

Answer 1

Step-by-step explanation:

let the two digits of a two digit number be X and Y.

Then the two digit number so formed is (10x+y),where X is at 10's place and Y is at unit place.

By question,

4 (X+y)=(10x+y)-18............(1)

And

4(X+y)=(10y+X)-9..............(2)

From above two equations we have,

10x+y-18=10y+x-9

Or,9x-9y-9=0

Or,x-y-1=0

Or,X=(1+y)

Using this value of X in (1) we get

4(1+y+y)=10(1+y)+y-18

Or,4+8y=10+11y-18

Or,12=3y

Therefore,y=4

Now X=(1+y)=1+4=5

Now required product of digits is

X*y=5*4= 20