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Let the number be xy, i.e. 10x + y
The number obtained on interchanging the positions of the digits will be yx, i.e. 10y + x
Difference between these two numbers = (10x + y) – (10y + x) = 9x – 9y = 9 (x – y) = 54
So, 9 (x – y) = 54
Or x – y = 6
So, statement 2 is correct.
The possible pair of such two-digit numbers are: (17, 71), (28, 82), (39, 93)
Respective product of their digits are: 1 × 7 = 7; 2 × 8 = 16; 3 × 9 = 27
So, we can determine the exact number-pair and hence the sum of their digits, if we know the product of their digits.
So, statement 1 is also correct.

By: Munesh Kumari

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Monika Bharti

Mam,the pair 39 and 93 when subtracted will only give 54 as the answer.So how can other options be correct ? What is the need of product if we can find answer without it. Should 1 be incorrect then?

Munesh Kumari

But other possibilities (17,28) are also there. We can say correct only if same value comes in all possibilities.