A number consists of three digits the right hand being zero if the left hand and the middle digits interchange the number is dismissed by 180 if the left hand digit behalf in the middle and right hand digits are interchanged the number is dismissed
Answers
Answer:
Since the number contains three digits, it has a hundreds place, a tens place and a ones place.
It is given that the right most digit is 0. Let the digits in the hundreds place and tens place be x and y respectively. Thus, the number is 100x + 10y + 0 = 100x +10y.
It is also given that if the digits in the hundreds place and tens place are interchanged, the difference between the original number and the new number after interchange is 180.
=> 100x + 10y - (100y + 10x) = 180
=> 100x + 10y - 100y - 10x = 180
=> 90x - 90y = 180
=> 90(x - y) = 180
=> x - y = 2 ---> (i)
It is also given that if the digit in the hundreds place is halved and digits in tens place and ones place are interchanged, the difference between the original number and the new number after interchange is 180.
=> 100x + 10y - (100x/2 + 0 + y) = 454
=> 100x + 10y -50x -y = 454
=> 50x + 9y = 464 --->(ii)
Multiplying both sides of Eqn (i) by 50, we get
50x - 50y = 100
Eqn (i) - Eqn (ii) => (50x - 50y) - (50x + 9y) = 100 - 454
=> 50x -50y -50x -9y = -354
=> -59y = -354
=> y = 6
Now, substitute the value of y in the equation x - y = 2.
=> x - 6 = 2
=> x = 8
Therefore, the three digit number xy0 = 860.