Question

A three -digit number is equal to seventeen times the sum of the digits. If the digits are reversed the new number is 198more than the original number the sum of extreme digits is 1less than middle digit. Find the original number. ​

Answer 1

Let the number be abc

So, number is 100a + 10b + c

• 100a + 10b + c = 17( a + b + c)

• 83a = 7b + 16c - - - - - - - - - - - (1)

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

= 198 + 99a = 99c

Hence, c - a = 2 ; c = a + 2- - - - - - (2)

Now, as a+c = b-1 and c = a+2

• a + a + 2 = b - 1

• b = 2a + 3

Now, substitute the values of b and c in eq. (1)

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

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