Question

a three digit number is 17 times the sum of the digits if the digits are reversed, then new number is 198 more than the old number, also the sum of extreme digits is less than the middle digit by unity. find the number​

Answer 1

Answer:

Let the number be abc

So number is 100a+10b+c

⇒100a+10b+c=17(a+b+c)

⇒83a=7b+16c .......(i)

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

Or 198+99a=99c

Hence c−a=2⇒c=a+2 .....(ii)

Also, given a+c=b−1

Now as a+c=b−1 and c=a+2

⇒a+a+2=b−1

⇒b=2a+3

now in eq(i)

substitute 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

So the number is 153