1.

Product of digits of a 2-digit number is 18. If we add 63 to the number, the new number obtained is a number formed by interchange of the digits. Find the number.1). 922). 293). 364). 63

Answer»

Let the number be xy

x × y = 18----(1)

10X + y + 63 = 10y + x

⇒ 9x + 63 = 9y

x + 7 = y----(2)

From (1) and (2) we get

⇒ x(x + 7) = 18

⇒ x2 + 7X – 18 = 0

(x + 9)(x – 2) = 0 ⇒ x = 2 as it can’t be negative

2Y = 18 ⇒ y = 9

The number is 29


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