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A three digit number is equal to 17 times the sum of its digits. If 198 is added to the number, the digits are interchanged. The addition of first and third digit is 1 less than middle digit. Find the number.

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The correct answer is 153 

100a+10b+c=17×(a+b+c)    -----(1)

100a+10b+c+198=a+10b+100c ---(2)

99a-99c=-198 

a-c=-2     ---(3)

... c=a+2    ----(4) 

a+c=b-1 ---(5) 

2a-b=-3 

2a+3=b 

 

In equation 1

100a+20a+30+c=17(a+2a+3+c)

100a+20a+30+a+2=17(a+2a+3+a+2)

53a=53

a=53 ---

C=1+2=3

b=2+3=5

Hence answer is 

100+50+3=153

 

 

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