Question

A number consists of two digits in which the tens digit exceeds the units digit by 6. The number itself is equal to ten times the sum of digits. Find the number.

Answer 1

Hint: The algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. From the given data we need to form equations i.e., linear equations as there is a constant variable involved and to solve the obtained equation, combine all the like terms and then simplify the terms to get the value of the number.

Complete step-by-step solution:
As given, a number consists of two digits in which the tens digit exceeds the units digit by 6 and the number itself is equal to ten times the sum of digits.
Let us consider the number as:
 \[10y + x\]
Where, x is the unit digit and y is the ten's digit, then by the given question we have:
\[y = x + 6\]
\[10y + x = 10\left( {x + y} \right)\]
Simplifying the terms, we get
\[10y + x = 10x + 10y\]
\[x - 10x = 0\]
\[ \Rightarrow x = 0\]
\[y = 0 + 6\]
\[ \Rightarrow y = 6\]
Substitute the obtained value of x and y as:
\[10y + x\] = \[10 \times 6 + 0 = 60\]

Hence, the given number is 60.

Note: The key point to solve the given question is that we must form the equations carefully such that as mentioned tens digit exceeds the units digit by 6, hence we must know the how to assign the number in the equation, such that to find the number we must consider the main data as the number itself is equal to ten times the sum of digits, hence based on this we can form equation and find the number.