A two digit number is such that the product
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a two digit number is such that the product of its digits is 18.when 63 is subtracted from the number,the digits interchange their places.find the number.
Answered by admin @
Answer:
Step-by-step explanation:
Solution :-
Let the tens place digit be x.
And the units place digit be y.
According to the Question,
⇒ xy = 18
⇒ y = 18/x .....(i)
And, (10x + y) - 63 = 10y + x
⇒ 9x - 9y = 63
⇒ x - y = 7 .... (ii)
Putting y's value in Eq (ii), we get
⇒ x - 18/x = 7
⇒ x² - 18 = 7x
⇒ x² - 7x - 18 = 0
⇒ x² - 9x + 2x - 18 = 0
⇒x(x - 9) + 2(x - 9) = 0
⇒ (x - 9) (x + 2) = 0
⇒ x - 9 = 0 or x + 2 = 0
⇒ x = 9, - 2 (As x can't be negative)
⇒ x = 9
Putting x's value in Eq (i), we get
⇒ xy = 18
⇒ 9y = 18
⇒ y = 18/9
⇒ y = 2
Number = 92
Hence, the required number is 92.
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