**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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**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.**

+1 vote

Best answer

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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