Question

1 who am i a 2-digit number. The tens digit is half of one’s digit.
2 I am smaller than half of 100. The difference of two digits is same as the digit at tens place.
3 Together the digits have a sum of 12.

Answer 1

Answer:

48

Step-by-step explanation:

1) 12/24/36/48

2) correct for all in (1)

3) 4+8=12

Answer 2

Given,

(a) A two-digit number where the tens digit is half of one’s digit.

(b)The number is smaller than half of 100 and the difference between two digits is the same as the digit at tens place.

(c) Together the digits have a sum of $\[12.\]$

To find,

The number formed from the given condition.

Solution,

Assume that the number is $\[10a + b.\]$

Therefore, from condition (a)

$\[ \Rightarrow a = \frac{b}{2}\]$

Therefore, from condition (b)

$\[\begin{array}{l} \Rightarrow 10a + b < \frac{{100}}{2}\\ \Rightarrow 10a + b < 50\end{array}\]$

Similarly,

$\[\begin{array}{l} \Rightarrow b - a = a\\ \Rightarrow 2a = b\end{array}\]$

Therefore, from condition (c)

$\[ \Rightarrow a + b = 12\]$

So,

$\[\begin{array}{l} \Rightarrow a + 2a = 12\\ \Rightarrow 3a = 12\\ \Rightarrow a = \frac{{12}}{3}\\ \Rightarrow a = 4\end{array}\]$

And,

$\[\begin{array}{l} \Rightarrow b = 2a\\ \Rightarrow b = 2 \times 4\\ \Rightarrow b = 8\end{array}\]$

Hence, the required number is $\[48.\]$