Question

B. A two-digit number can be expressed as
8 times the sum of its digits increased by
1. as well as, 13 times the difference of its
digits increased by 2. Find that number.​

Answer 1

Answer:

41

Step-by-step explanation:

let the 2 digits of the number be x & y

given that 10x+y = 8(x+y)+1

=> 10x + y = 8x+8y+1

=> 10x-8x+y-8y = 1

=> 2x-7y=1 ---------------- 1

also,

given that 10x+y = 13(x-y)+2

=> 10x-13x+y+13y=2

=> -3x+14y = 2 ------------ 2

solving 1 & 2 ,

(1) * 3 =>   6x - 21y = 3

(2) * 2 => -6x+28y = 4

(+)

-------------------------------------

                      7y = 7

=> y = 7/7 = 1

substitute the value of y in 1,

2x -7(1) = 1

2x -7 = 1

2x =1+7

2x=8

=>x = 8/2 = 4

x=4

therefore the 2 digit number is 10(4)+1 = 40+1 = 41