The sum of the digits of a two-digit number is 5. If the digit obtained by increasing the digit in ten’s place
The sum of the digits of a two-digit number is 5. If the digit obtained by increasing the digit in ten’s place by unity is one-eighth of the number, then the number is ……………….
A) less than 30
B) lies between 30 and 40
C) more than 37
D) lies between 40 and 50
2 Answers
Correct option is (B) lies between 30 and 40
Let the two-digit number be ab where a is 10's digit and b is unit digit.
\(\therefore\) ab = 10a + b __________(1)
\(\because\) Sum of digits is 5.
\(\therefore\) a+b = 5 __________(2)
According to \(2^{nd}\) condition, we have
a+1 \(=\frac18(10a+b)\)
\(\Rightarrow\) 8a+8 = 10a+b
\(\Rightarrow\) 2a+b = 8 __________(3)
Subtract equation (2) from (3), we get
(2a+b) - (a+b) = 8 - 5
\(\Rightarrow\) a = 3
\(\therefore\) b = 5 - a
= 5 - 3 = 2
Hence, the number is ab = 32 which lies between 30 and 40.