Question

31] A two digit number is obtained by multiplying the sum of the digits by 8 and adding one
or multiplying the difference of the digits by 13 and adding two. Find the number,​

Answer 1

Answer:

The 2- digit number is 41

Step-by-step explanation:

Let the 2- digit number be 10 x + y

10 x + y =  8(x + y) +1

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

2 x -7 y - 1 =0                                                  Eq 1

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

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

3 x - 14 y +2 = 0                                                Eq 2

Eq 1 ×2                       4 x -14 y -2 = 0

Eq 2 × (-1)                 -3 x +14 y -2 = 0

=                                 x   - 4 = 0

x = 4

Substituting ' x ' in Eq 1 ,

2 x - 7 y - 1 = 0

8 - 7 y - 1 = 0

7 y = 7

y = 1

Therefore the number is , 10 × 4 + 1 = 41