A two-digit number is formed by either subtracting 17 from nine times the sum of the digits or by adding 21 to 13 times

Correct option is (A) 73

Let two-digit number be ab where b is unit's digit and a is ten's digit.

\(\therefore\) ab = 10a + b       __________(1)

According to first condition

10a + b = 9 (a+b) - 17

\(\Rightarrow\) 10a - 9a + b - 9b = -17

\(\Rightarrow\) a - 8b = -17        __________(2)

According to second condition

10a + b = 13 (a - b) + 21

\(\Rightarrow\) 10a - 13a + b + 13b = 21

\(\Rightarrow\) -3a + 14b = 21  __________(3)

Multiply equation (2) by 3, we get

3a - 24b = -51       __________(4)

By adding equations (3) & (4), we get

14b - 24b = 21 - 51

\(\Rightarrow\) -10b = -30

\(\Rightarrow b=\frac{-30}{-10}=3\)

Then from (2), we obtain

a = 8b - 17 = 24 - 17 = 7

\(\therefore ab=10\times7+3=73\)

Hence, required number is 73.

Correct option is A) 73