a single digit in a two-digit number is 5. find the number if the number is 5 times the sum of the two digits?
Answers
Answer:
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Step-by-step explanation:
Solution :-
Let the tens place digit of required number be x.
And the unit place digit be y.
According to the Question,
⇒ 10x + y = 5(x + y)
⇒ 4y = 5x
⇒ y = 5x/4 .... (i)
And, 10x + y = 2xy + 5
⇒ 10x + 5x/4 = 2x × 5x/4 + 5 [From (i)]
⇒ 45x/4 = 10x²/4 + 5
⇒ 10x² - 45x + 20 = 0
⇒ 2x² - 9x + 4 = 0
⇒ 2x² - 8x - x + 4 = 0
⇒ 2x(x - 4) - 1(x - 4) = 0
⇒ (x - 4) (2x - 1) = 0
⇒ x - 4 = 0 or 2x - 1 = 0
⇒ x = 4, 1/2 (As x can't be a fraction)
⇒ x = 4
Putting x's value in Eq (i), we get
⇒ y = 5x/4
⇒ y = 5(4)/4
⇒ y = 20/4
⇒ y = 5
Number = 45
Hence, the required number be 45.
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Step-by-step explanation:
first number is 5 then second number is 5 times of 5 so 5×5 = 25 so the sum of 2 digit is 25+5 = 30