Question

A two digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 5 or by multiplying the difference of the digits by 16 and then adding 3 find the number.

Answer 1

Answer:

83

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 = 8(x+y) - 5

10y + x = 8x + 8y = - 5

7x - 2y = 5 -------- i)

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

10y + x = 16 (y-x) + 3

10y + x = 16y - 16x + 3

17x - 6y = 3 -------- ii)

multiply eq(1) by 3 and subtracting eq(2):

21x - 6y = 15

17x - 6y = 3

4x = 12

x = 12 / 4 = 3

substitute x = 3 in eqn (1).

7* 3 - 2y = 5

2y = 21 - 5

2y = 16

y = 16 / 2 = 8

thus the unit digit of the number is 3 and ten's digit is 8 .

thus number is 83