Question

A number consists of three digits of which the middle one is 0. If the left hand and right hand digits are interchanged the number is decreased by 198. If the left hand digit is halved and the middle and right hand digits be interchanged, the number is diminished by 228. Find the number.

Answer 1

Let no. at unit's place be x
Let no. at tens place be 10y
Let no. at hundred's place be 100z
Also let The NO. = a
A.T.Q, 10y=0 .^..y=0........(i)
Also 100z+10y+x =a..............(ii)
NOW,A.T.Q
100x+10y+z = a+198 .........(iii)
SUBTRACTING (iii)FROM (ii)
100z + 10y + x =+ a
+ z + 10y + 100x = +a+198
^{- - - - -}
99z-99x=-198
z-x=-2......(iv)
ALSO,A.T.Q
50z+y+10x = a-228……(v)
SUBTRACTING(v) from (ii)
100z+10(0)+x-50z-(0)-10x
=a-a+228(^..^. y=0)

50z-9x=228........(vi)
Putting in(vi)
50z-9(z+2)=228
=>z=6
PUTTING in (vii)
x=6+2=8
THEREFORE NO.=100z+10y+x=608