A two digit number is such that a product of its digits is 35 .When 18 is added to rhe number the digit interchange their places .Find the number
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Let the digit in tens place be x and ones place be y
xy=35
The number=10x+y
After interchanging digits no=10y+x
ATQ
10x+y+18=10y+x
On solving we get
=>y=x+2
Putting in eq xy=35
x(x+2)=35
x^2+2x=35
x^2+2x-35=0
x^2+x(7-5)-35=0
x^2+7x-5x-35=0
x(x+7)-5(x+7)=0
(x-5)(x+7)=0
x=5 or x=-7
y=x+2=7
The no is 10x+y
10×5+7=57
xy=35
The number=10x+y
After interchanging digits no=10y+x
ATQ
10x+y+18=10y+x
On solving we get
=>y=x+2
Putting in eq xy=35
x(x+2)=35
x^2+2x=35
x^2+2x-35=0
x^2+x(7-5)-35=0
x^2+7x-5x-35=0
x(x+7)-5(x+7)=0
(x-5)(x+7)=0
x=5 or x=-7
y=x+2=7
The no is 10x+y
10×5+7=57
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