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,
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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
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