Experts,
MeritNation
- Varun Rawat sir had asked me to recheck the below question and to get back, so here I am ... again asking the same question with the necessary corrections:
QUESTION:
A number consists of 3 digits whose sum is 7. The digit at the units place is twice the digit at ten's place. If 297 is added to the number, the digits of the number are reversed. Find the number.
{Please don't provide any weblink or any certified answer ... Please give a answer with a proper explanation}
Dear Student,
Please find below the solution to the asked query:
Given :A number consists of 3 digits , the digit at the units place is twice the digit at ten's place. So we assume ,
Ten's place digit = x , So
Unit's place digit = 2 x
And
Hundred's place digit = y
So, Our number = 100 y + 10 x + 2 x = 100 y + 12 x --- ( 1 )
Also given : A number consists of 3 digits whose sum is 7. So
y + x + 2 x = 7 ,
3 x + y = 7 --- ( 2 )
And given : If 297 is added to the number, the digits of the number are reversed. So
100 y + 10 x + 2 x + 297 = 100 ( 2 x ) + 10 x + y ,
100 y + 12 x + 297 = 200 x + 10 x + y ,
198 x - 99 y = 297 ,
99 ( 2 x - y ) = 297 ,
2 x - y = 3 --- ( 3 )
Now we add equation 2 and 3 we get :
5 x = 10 ,
x = 2 , Substitute that value in equation 1 we get :
3 ( 2 ) + y = 7 ,
6 + y = 7 ,
y = 1
We substitute values of ' x ' and ' y ' in equation 1 and get :
Our number = 100 ( 1 ) + 12 ( 2 ) = 100 + 24 = 124 ( Ans )
Hope this information will clear your doubts about topic.
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards
Please find below the solution to the asked query:
Given :A number consists of 3 digits , the digit at the units place is twice the digit at ten's place. So we assume ,
Ten's place digit = x , So
Unit's place digit = 2 x
And
Hundred's place digit = y
So, Our number = 100 y + 10 x + 2 x = 100 y + 12 x --- ( 1 )
Also given : A number consists of 3 digits whose sum is 7. So
y + x + 2 x = 7 ,
3 x + y = 7 --- ( 2 )
And given : If 297 is added to the number, the digits of the number are reversed. So
100 y + 10 x + 2 x + 297 = 100 ( 2 x ) + 10 x + y ,
100 y + 12 x + 297 = 200 x + 10 x + y ,
198 x - 99 y = 297 ,
99 ( 2 x - y ) = 297 ,
2 x - y = 3 --- ( 3 )
Now we add equation 2 and 3 we get :
5 x = 10 ,
x = 2 , Substitute that value in equation 1 we get :
3 ( 2 ) + y = 7 ,
6 + y = 7 ,
y = 1
We substitute values of ' x ' and ' y ' in equation 1 and get :
Our number = 100 ( 1 ) + 12 ( 2 ) = 100 + 24 = 124 ( Ans )
Hope this information will clear your doubts about topic.
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards