When digits of a two digit number are interchanged then it becomes 54 more than the original number ...........

Quantitative Aptitude (SBI-PO) Number System

When digits of a two-digit number are interchanged, then it becomes 54 more than the original number. The product of the two digits is 16. What is the original number?

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Explanation:

Let the number be xy.
According to question,
10y + x – (10x + y) = 54
⇒ 9y – 9x = 54
⇒ y – x = 6 ⇒ y = (6 + x) …..(1)
Also, xy = 16 …..(2)
From (1) and (2) we get:
x(6 + x) = 16
⇒ x = 2
Thus, y = 2 + 6 = 8
Original number = 28