Question

A number a number consists of three digit the right hand digit begin zero is the left left hand digit in the middle digit be interchanged the number is deminshed by 180 if the left-hand digit be halved in the middle and right hand digits interchange the number is deminshed by 454 find the number

Answer 1

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