if a two-digit number is divided by the sum of the digits, the quotient is 6 and the reminder 8. if the number is divided by the product of the digit, the quotient is 2 and the remainder 18. Find the number.
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Let the two digit number be 10x+y and number obtained by interchanging the digit =10y+x
As per the first condition,
10x+y=6(x+y)+3
4x−5y=3...(i)
As per the second condition,
10y+x=4(x+y)+9
−3x+6y=9...(ii)
Multiplying equation (i) by 3 and (ii) by 4 and adding them, we get
12x−15y=9
−12x+24y=36
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9y=45
y=5
Substitute y=5 in equation (i)
4x−5×5=3
4x=28
x=7
So, the number =10x+y=10×7+5=75
Step-by-step explanation:
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