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) 73 B) 79 C) 81 D) 92
Answer» 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

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) 73 B) 79 C) 81 D) 92

Answer»

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