A two-digit number is five times the sum of its digits and is also equal to 5 more than twice the
product of its digits. Find the number.
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Answered by
0
Answer:
55 is the answer for this
Answered by
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Answer:
Step-by-step explanation:
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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