SOLUTION: In a three digit number the sum of the digits at hundreds place and units place is equal to the digit at the tens place. The original number is 22 times the sum of its three digits

Question 875471: In a three digit number the sum of the digits at hundreds place and units place is equal to the digit at the tens place. The original number is 22 times the sum of its three digits. If 297 is added to the original number the order of the digits is reversed. Find the original number

Answer by dkppathak(439) (Show Source): You can put this solution on YOUR website!
In a three digit number the sum of the digits at hundreds place and units place is equal to the digit at the tens place. The original number is 22 times the sum of its three digits. If 297 is added to the original number the order of the digits is reversed. Find the original number
let hundred place is X tens place is Y and one place is Z
as per given condition
X+ Z =Y (1)
as per second conditions
100X + 10 Y +z =22( x+Y+Z)
78X-12Y-21Z=0 (2)
as per third condition
100X + 10 Y +z +297=( x+10Y+100Z) (3)
99x-99z=-297 by taking 99 common
X-Z =-3 (3)
by substituting value of Y from 1 in equation 2
78X-12 (x+Z)- 21Z =0 (2)
78X-12X-12Z-21Z =0
66X-33Z =0 by taking 33 common
2x -Z =0 (4) by solving equation (3) and (4)
x=3 and Z =6
by substiting value of x and Z in (1)
y=x+Z =3+6 =9 Y=9
number will be hundred place 3 tens place 9 and one place 6
number will be 396 which will satisfy all three conditions
Answer 396

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