sum of digits of a 2 digit number is 9. if the digits are reversed, the new number is 9 less than 3 times the original number. find the original number
Answers
SOLUTION:-
Given:
•Sum of digits of a two number is 9.If the digits are reversed, the new number is 9 less than 3 times the original number.
To find:
The original number.
Explanation:
Let the digit of ones place be R.
Let the digit of tens place be M.
- Original Number=10R + M
- Reversed number=10M+ R
According to the question:
R + M= 9
R=9 - M..............(1)
=) 10M +R -9 = 3(10R +M)
=) 10M + R -9 = 30R + 3M
=) 10M -3M+ R -30R= 9
=) 7M -29R= 9
=) 7M - 29(9 - M) =9 [Using equation (1)]
=) 7M - 261+ 29M =9
=) 36M -261 =9
=) 36M = 9 +261
=) 36M = 270
=) M= 270/36
=) M= 7.5
&
Putting the vakue of M in equation (1), we get;
R= 9 - 7.5
R= 1.5
Thus,
The original number: 10R + M
=) 10(1.5) + 7.5
=) 15 + 7.5
=) 22.5
Answer:
Original number is 27.
Step-by-step explanation:
Since we know that the sum of the two digits in the original number and the new number is 9 , we can write the original number and the new number as :-
Tens Ones
Original Number 9 - x x
New number x 9 - x
Now that we found out the tens and ones place , we can multiply the digit in the tens place with ten and add it with the digit in the ones place.
Original number = 10(9 - x) + x
= 90 - 10x + x
=90 - 9x
New number = 10(x) + 9 - x
= 10x + 9 - x
= 9x + 9
Now that we know that original number = 90 - 9x , and the new number = 9x + 9 ,
we can understand what "x" is .The question says that the new number is 9 less than 3 times the original number .So we can phrase it like this :-
9x + 9 = 3(90 - 9x) - 9
9x + 9 = 270 - 27x - 9
9x + 9 = 261 - 27x
Now we transpose ,
9x + 9 = 261 - 27x
9x + 27x = 261 - 9
36x = 252
x = 252/36
x = 7
We have found that x = 7 ,
But the question is to find the original number , so now that we now the value of "x" ,
the original number = 90 - 9x
= 90 - 9(7)
= 90 - 63
= 27
Therefore the original number is 27
:)