A two digit number is five times the sum of its digits. If 9

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RRB TC CC Exam (Bangalore) 2007 click here to view all questions

A two digit number is five times the sum of its digits. If 9 is added to the number, the digits interchange. Find the sum of the digits.

A11

B7

C6

D9

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Let a and b the digits we can write the number as "ab" but the number is $10 \times a+b$ (for example if a=3 and b=2 the number would be 32 and $32 =10 \times 3+2$)  a two digit number is 5 times the sum of its digit then $10 \times a+b=5(a+b)$ when 9 is added to the number the result is the original number with its reversed $10 \times a+b+9=10 \times b+a$ then we have the following equations:  $10 \times a+b=5(a+b)$ $10 \times a+b+9=10 \times b+a$ then  $10a+b=5a+5b$ $10a+b+9=10b+a$ then  $5a-4b=0$   $9a-9b=-9$ then  $5a-4b=0$ $a-b=-1$ then using 2nd eq a=b-1  using 1st eq $5(b-1)-4b=0$ then $5b-5-4b=0$ then b=5 and a=5-1=4  the sum of digits is 9. quiaz ? answered Dec 20 '2018 at 14:16 All Comments

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