Question

3. A certain number between 10 and 100 is 8 times the sum of its digits, and if 45 be subtracted from it the
digits will be reversed. Find the number.​

Answer 1

since the number is between 10 and 100 the required number is a number is a two digit number

let x be in ten's place in y b in unit's place

the number can be written as 10x + y

as per the giving conditions

=>10x + y = 8 (x + y)

=>10x + y = 8x + 8y

=>2x - 7y = 0..............(1)

and

=>10x + y - 45 = 10y + x

=>9x - 45 = 9y

=>x - y = 5..................(2)

solving 1 and 2 we get

2x - 7y = 0

2x - 2y = 10

...................

-5y = - 10

y = 2

from eq 2

x = 5+2 = 7

therefore the required no. is

=7 x 10 + 2

= 72