Question

In a two digit number, the digit at tens place is 7 and sum of digits is 8 times the digit at unit place. Then the number is
A) 17
B) 71
C) 70
D) 78

Answer 1

Hint: First we assume the digit at unit’s place as x and then find its value with the help of given conditions. Then, find the number by applying the following formula:
\[{{number = 10 \times }}\left( {{\text{digit at tens place}}} \right) + \left( {{\text{digit at unit place}}} \right)\]

Complete step-by-step answer:
Let the digit at unit’s place be x
Since, the digit at tens place is 7
Therefore, the sum of digits at tens place and unit place is:- \[7 + x\]
Since it is given that the sum of digits is 8 times the digit at unit place
Therefore, we will form a linear equation in one variable according to the given condition to get the value of x.
Hence,
\[7 + x = 8\left( x \right)\]
\[7 = 8x - x\]
\[7x = 7\]
\[ \Rightarrow x = \dfrac{7}{7}\]
\[\therefore x = 1\]
Now, since we got the value of digit a unit’s place therefore, Putting the respective values in the following formula:-
\[{{number = 10 \times} \left( {{\text{digit at tens place}}} \right) + \left( {{\text{digit at unit place}}} \right)}\]
We get:-
\[{\text{number}} = {{10 \times }}\left( {\text{7}} \right) + \left( {\text{1}} \right)\]
\[{\text{number}} = 70 + 1\]
\[{\text{number}} = 71\]
Hence the resulting number is 71

Therefore, option (b) is the correct option.

Note: A linear equation in one variable is an equation in which maximum power of the variable is 1 and has only one variable and is of the following form:
\[ax + b = 0\]
It represents the equation of a straight line.
The student should multiply the digit at ten’s place by 10 and the digit at unit’s place by 1 in order to get the correct number.