Question

A two digit number is obtained by either multiplying sum of the digits by 9 and subtract 4 by multiplying the difference of the digits by 12 and adding 5.find the number?

Answer 1

Step-by-step explanation:

let the unit digit and the ten's digit of the number be x and y respectively.

therefore the number = 10y + x.

sum of digits = x+y

10y + x = 9(x+y) - 4

10y + x = 9x + 9y - 4

8x - y = 4 -------- i)

difference of the digits = y-x [if x<y ]

10y + x = 12 (y-x) + 5

10y + x = 12y - 12x + 5

13x - 2y = 5 -------- ii)

multiply eq(1) by 2 and subtracting eq(2):

16x - 2y = 8

13x - 2y = 5

3x = 3

x = 3 / 3 = 1

substitute x = 1 in eqn (1).

8* 1 - y = 4

-y = 4-8

y = 4

thus the unit digit of the number is 1 and ten's digit is 4 .

thus number is 41