A no. consists of 3 digits , the right hand being zero. If the left hand and middle digits be interchanged the no. is diminished by 180.If the left hand digit be halved and middle and right hand digits be interchanged the no. is diminished by 454. Find the no. .
Suppose the digits at ten's place is x
and the digit at hundred's place is y.
And the digit at unit's place is 0 as per question.
So the number is 100y + 10x + 0 = 100y + 10x
when the left hand and middle digits be interchanged
New number = 100x + 10y
According to question, when the left hand and middle digits be interchanged the no. is diminished by 180, so we have;
Now when the left hand digit be halved and middle and right hand digits be interchanged;
The number is i.e. 50y + x
And according to the question,when the left hand digit be halved and middle and right hand digits be interchanged the no. is diminished by 454, so we have;
So from (i) and (ii) we get;
x = 6 and y = 8
so the number is (100y + 10x) = = 860
and the digit at hundred's place is y.
And the digit at unit's place is 0 as per question.
So the number is 100y + 10x + 0 = 100y + 10x
when the left hand and middle digits be interchanged
New number = 100x + 10y
According to question, when the left hand and middle digits be interchanged the no. is diminished by 180, so we have;
Now when the left hand digit be halved and middle and right hand digits be interchanged;
The number is i.e. 50y + x
And according to the question,when the left hand digit be halved and middle and right hand digits be interchanged the no. is diminished by 454, so we have;
So from (i) and (ii) we get;
x = 6 and y = 8
so the number is (100y + 10x) = = 860