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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 ofits digits, the quotient is 6 with no remainder. When the number isdiminished by 9, the digits are reversed. Find the number. [CBSE 1999C) |
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Answer» 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 |
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