Question

A no. consists of 2 digits when it is divided by the sum of digits the quotient is 6 with no remainder. When the no. is diminished by 9 the digits are reversed. Find the nos.

Answer 1

as the no reverses by subtracting 9 so right minus left should be -1 and no. must be a multiple of 6 so 54 is the ans.

Answer 2

We know that Dividend=Divisor×Quotient+Remainder

Let the tens and the units digits of the required number be x and y,Respectively.

Required number=10x+y

10x+y=(x+y)×6+0

⇒10x−6x+y−6y=0

⇒4x−5y=0 ...(1)

Number obtained on reversing its digits=10y+x

∴10x+y−9=10y+x

⇒9x−9y=9 or x−y=1 ...(2)

On multiplying (2) by 5, we get

5x−5y=5 ...(3)

On subtracting (1) from (3),we get

x=5

On substituting x=5 in (1), we get

4×5−5y=0

⇒20−5y=0

⇒y=4

∴The number =10x+y=10×5+4=50+4=54

Hence the required number is 54