Question

The sum of the digits of the three digit numbers is 11. The sum of first and third digit is more than 1 by the middle digit. If 198 is added to the number then the digit are of the number are interchanged, then find the numbers.​

Answer 1

Step-by-step explanation:

number is 100a+10b+c

⇒100a+10b+c=17(a+b+c)

⇒83a=7b+16c .

198+100a+10b+c=a+10b+100c

Or 198+99a=99c

Hence c−a=2⇒c=a+2

⇒a+a+2=b−1

⇒b=2a+3

now in eq(i)

the values of b and c

83a=7b+16c

⇒83a=7(2a+3)+16(a+2)

⇒53a=21+32

⇒a=1

⇒c=a+2=3

⇒b=2a+3=5

Answer:-153