Atwo digit number is obtained by either multiplying sum of the digits by 8 or adding 1or by multiplying the difference of the digits by 13 and adding 2.find the number.

Asked by Praveen Kumar | 15th Jul, 2013, 12:27: PM

Expert Answer:

Let the two digit number be 10x + y

From the given conditions, we have:

10x + y = 8 (x + y) + 1 = 8x + 8y + 1

? 8y – y = 10x – 8x – 1

? 7y = 2x – 1  ........(1)

and 10x + y = 13 (x – y) + 2 = 13x – 13y + 2

? 13x – 10x – 13y – y = – 2

? 3x – 2 × 7y = – 2

? 3x – 2 (2x – 1) = – 2  (from (1))

? 3x – 4x + 2 = – 2

? – x = – 2 – 2

? x = 4

? 7y = 2 × 4 – 1 = 7

Hence the required number is 10 × 4 + 1 = 41

Answered by  | 15th Jul, 2013, 05:44: PM

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