A two-digit number is formed by either subtracting 17 from nine times

1.	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 the difference of the digits. Find the number. A) 37 B) 73 C) 75 D) 57
Answer» 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. Correct option is B) 73

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 the difference of the digits. Find the number. A) 37 B) 73 C) 75 D) 57

Answer»

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.

Correct option is B) 73