Correct option is (B) 73
Let required two-digit number be ab or (10a+b).
Sum of digits = a+b
According to given conditions, we have
10a+b = 9 (a+b) - 17
\(\Rightarrow\) 10a - 9a + b - 9b + 17 = 0
\(\Rightarrow\) a - 8b + 17 = 0 ______________(1)
And 10a+b = 13 (a - b) + 21
\(\Rightarrow\) 10a - 13a + b + 13b - 21 = 0
\(\Rightarrow\) -3a + 14b - 21 = 0 ______________(2)
From (1) & (2), we obtain
-3 (8b - 17) + 14b - 21 = 0
\(\Rightarrow\) -24b + 51 + 14b - 21 = 0
\(\Rightarrow\) -10b + 30 = 0
\(\Rightarrow b=\frac{30}{10}=3\)
\(\therefore\) a = 8b - 17 (From (1))
= 24 - 17 = 7
\(\therefore\) Required two-digit number is ab = 73.
