Question

The digit in the tens place of a two digit number is four times the digit in the units place. When the digits are reversed, the number obtained is 27 less than the original number. Find the original number.

Answer 1

Hint:
Here in this question we have to use a simple calculation to find out the original number. Firstly we have to note down all the conditions given in the question and by simply solving those conditions we will be able to find out the original number.

Complete step by step solution:
Let \[{\rm{XY}}\]be the original number, which means X is the tens place digit and Y is the unit place digit.
So, we can write it as \[{\rm{XY = 10X + Y}}\]
It is given in the question that tens place of a two digit number is four times the digit in the units place i.e. \[{\rm{X = 4Y}}\]
Now when the number is reversed we get \[{\rm{YX}}\] which can be written as \[{\rm{YX = 10Y + X}}\]
So, according to the question when the digits are reversed, the number obtained is 27 less than the original number which means
\[{\rm{YX = XY}} - 27\]
Now putting the value of XY and YX in the above equation, we get
\[ \Rightarrow {\rm{10Y + X}} = {\rm{10X + Y}} - 27\]
\[ \Rightarrow {\rm{9X = 9Y}} + 27\]
Now, we know that \[{\rm{X = 4Y}}\] so putting the value of X in the above equation, we get
\[ \Rightarrow {\rm{9(4Y) = 9Y}} + 27\]
\[ \Rightarrow 36{\rm{Y}} - {\rm{9Y}} = 27\]
Therefore by solving this equation we will get the value of Y
\[ \Rightarrow 27{\rm{Y}} = 27\]
\[ \Rightarrow {\rm{Y}} = 1\]
So, we know that \[{\rm{X = 4Y}}\] we also get the value of the X by putting the value of Y in it
\[ \Rightarrow {\rm{X}} = 4\]
Therefore, the original number is \[{\rm{XY = 10X + Y}} = {\rm{10(4) + 1 = 40 + 1 = 41}}\]

Hence, 41 is the original number.

Note:
In the two digits number there is always a tens place digit and a unit place digit. Maximum two digits number is 99 and minimum two digits number is 10.In the three digits number there is always a hundreds place digit, a tens place digit and a unit place digit. Maximum three digits number is 999 and minimum two digits number is 100 and similarly for the four digits number it goes on.
Even numbers are any integer that can be divided exactly by 2 is an even number. The last digit is 0, 2, 4, 6 or 8.Odd numbers are the numbers that cannot be divided by 2. The last digit is 1, 3, 5, 7 or 7.