Question

added to the number, the digits are reversed. Find the number.
18. A number consists of two digits. When it is divided by the sum of
its digits, the quotient is 6 with no remainder. When the number is
diminished by 9, the digits are reversed. Find the number. [CBSE 1999C)​

Answer 1

We know: 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 …….(i)

==>> Number obtained on reversing its digits = (10y + x)

∴ 10x + y - 9 = 10y + x

⇒9x – 9y = 9

==> x – y = 1 ……..(ii)

On multiplying (ii) by 5, we get:

==> 5x – 5y = 5 ……..(iii)

On subtracting (i) from (iii), we get:

x = 5 On substituting x = 5 in (i) 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