+2 votes
19 views

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.

by
reopened by | 19 views

1 Answer

+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

 

 

by (3.1k points)
selected by
532 questions
525 answers
8 comments
12 users