On reversing the digits of a two digit number, number obtained is 9 less than three times
the original number. If difference of these two numbers is 45, find the original number.
Answers
Step-by-step explanation:
Given :-
On reversing the digits of a two digit number, number obtained is 9 less than three times the original number. and difference of these two numbers is 45.
To find :-
Find the original number ?
Solution :-
Let the digit in the 10's place in the two digit number be X
The place value of X = 10X
Let the digit in the 1's place in the two digit number be Y
The place value of Y = Y
The original two digit number = 10X+Y
On reversing the digits in the two digit number then the new number = 10Y+X
Given that
On reversing the digits of a two digit number, number obtained is 9 less than three times
the original number.
=> New number = 3× Original number - 9
=> 10Y+X = 3(10X+Y)-9
=> 10Y+X = 30X+3Y-9
=> 30X+3Y-10Y-X = 9
=> (30X-X) +(3Y-10Y) = 9
=> 29X +(-7Y) = 9
=> 29X -7Y = 9 ----------(1)
and
The diference of these two numbers = 45
=> New number - Original number = 45
=> (10Y+X) -(10X+Y) = 45
=> 10Y+X-10X-Y = 45
=> (10Y-Y)+(X-10X) = 45
=> 9Y-9X = 45
=>9(Y-X) = 45
=> Y-X = 45/9
=> Y-X = 5
=>Y = 5+x ---------(2)
On substituting the value of Y in (1) then
=> 29X -7Y = 9
=> 29X -7(5+X) = 9
=> 29X -35-7X = 9
=> (29X-7X)-35 = 9
=> 22X -35 = 9
=> 22X = 9+35
=> 22X = 44
=> X = 44/22
=> X = 2
And
On substituting the value of X in (2) then
=> Y = 5+2
=> Y = 7
Therefore ,X = 2 and Y = 7
The digit at 10's place = 2
The digit at 1's place = 7
Then the number = 27
Answer:-
The required original number for the given problem is 27
Check :-
Original number = 27
The new number obtained by reversing the digits= 72
Their difference = 72-27 = 45
New number = 72
=> 81-9
=> (3×27)-9
=> 3×Original number -9
New number = 3×Original number -9
Verified the given relations in the given problem.