The sum of two digit number and number formed by interchanging its digit is 110. If 10 is subtracted from the first number, the new number 4 more than 5 times the sum of the digit in the first number the first is..........
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Answer:
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Answer:
64
Step-by-step explanation:
Let the 2 digit number be 10x+y
Therefore,
Interchanged number = 10y+x
10x+y+10y+x = 110
=> 11(x+y) = 110
=> x+y = 10—(1)
10x+y - 10 = 5(x+y) + 4
=> 10x + y = 5x + 5y + 14
=> 5x - 4y = 14 —(2)
Multiplying (1) by 4 and adding to (2)40
4x+4y + 5x - 4y = 40 + 14
=> 9x = 54
=> x = 6
=> y = 10-x = 4
Therefore,
The number is 10x+y = 10×6+4 = 64
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