The product of digits of a two-digit number is 12. If the number is 36 more than the number obtained by reversing its digits, then the original number is
Answers
Answer:
62
Step by step explanation:
Let the digit in ones place be y and digit in tens place be 10x
Therefore,
The original number = 10x + y
If the digits are reversed the number becomes 10y + x
ATQ,
10x + y = 36 + (10y + x)
=> 10x + y = 36 + 10y + x
=> 10x - x + y - 10y =36
=> 9x - 9y =36
=> 9(x - y) = 36
=> x - y = 36/9 = 4
Multiplying x to both sides
⟹ x(x − y) = 4x
⟹ x² − xy = 4x
⟹ x² - 4x − 12= 0 (As xy = 12)
⟹ x² - 6x + 2x− 12=0
⟹ x(x - 6) + 2(x - 6)=0
⟹ x - 6 = 0
=> x = 6
We know that xy= 12,
Hence,
6 × y = 12
6 × y = 12
=> y = 12 /6
= 2
Therefore,
the original number = 10x + y
=60 + 2 = 62
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