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प्रश्न
A two digit number is such that the product of its digits is 16. If 54 is subtracted from the number, the digits are interchanged. Find the number.
बेरीज
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उत्तर
Let the two-digit number have tens digit = x and units digit = y.
Product of digits is 16:
xy = 16
Original number = 10x + y:
After subtracting 54, digits are interchanged:
10x + y − 54 = 10y + x
9x − 9y = 54
x − y = 6
xy = 16
x − y = 6
From x − y = 6,
x = y + 6
Substitute in xy = 16:
(y + 6)y = 16
y2 + 6y − 16 = 0
(y + 8) (y − 2) = 0
y = 2 or y = −8
x = y + 6 = 8
The two-digit number is:
82
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