Question

A number of three digits has five in the unit’s place and the middle digit is half
the sum of other two. If 108 be added to the number hundredth figure will take
the unit’s place and the unit’s the ten’s and the ten’s the hundred’s. Find the
number.​

Answer 1

Answer:

345

Step-by-step explanation:

let the 3 digits of the given number be a,b, and c respectively.

so, the number is 100a + 10b + c

given that c = 5

also, given b = (a+c)/2 = (a+5)/2

ie., 2b = a+5

=> a = 2b-5 ------- (1)

then, given that,

(100a + 10b + c) + 108 = 100b + 10c + a

ie., (100a + 10b + 5) + 108 = 100b + 10*5 + a

=> 100a-a +10b-100b = 50-113

=> 99a-90b = -63

by (1)

=>  99(2b-5) +90b = -63

=> 198b - 495 + 90b = -63

=> 108b = 495-63 = 432

=> b = 432/108 = 4

b=4

so, (1) => a = 2*4 - 5

                 = 8-5

                 = 3

ie., a = 3

so, the number is ,

(100*3) + (10*4) + 5

=> 300+40+5

=> 345