A number consists of three digit of which the middle one is 0 if the left hand and right hand digit be interchanged the number is increased by 198 if the left hand digit be halved and middle and the right digit be interchanged the number decresed by 228 find the number.
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.
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