Question

the sum of the digits of a number consisting of three digits is 12 the middle digit is equal to half the sum of the other two . if the order of the digits is reversed the number is diminished by 198. find the number.​

Answer 1

Answer:543

Step-by-step explanation:

Let the digits be 'x','y' and 'z'

So according to the question : x+y+z = 12 and y = (x+z)/2

substituting value of y,

x+ (x+z)/2 +z =12

⇒(2x+x+z+2z)/2 = 12

⇒3x+3z=24

⇒x+z=8  (eqn 1)

Part 2

100x+10y+z-198= 100z+10y+x

⇒99x-99z= 198

⇒x-z=2 ( eqn 2)

adding equation 1 and 2

⇒x+z+x-z=8+2

⇒2x=10

⇒x=5

Substituting x=5 in equation 1

⇒5+z=8

⇒z=3

∴The given number is,

100x+10y+z

=543