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Question

Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:
The sum of the digits of a two-dlgit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number

A
Number is 18
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B
Number is 36
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C
Number is 81
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D
None of these
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Solution

The correct option is B Number is 18
let the unit digit =x
Ten digit =y
Sum of two digits are 9
x+y=9 ........(1)
Number will 10 times the tens digit + unit times the unit digit
Number =10y+x
The number obtained by reversing the order of digit
10x+y
According to the second condition, we have
9(10y+x)=2(10x+y)
90y+9x=20x+2y
88y11x=0
Divide by 11,
8yx=0....... (2)

Adding both equation,
9y=9
y=1
Put y=1 in (1)
x+1=9x=8
Hence, the original number is 10y+x=10×1+8=18.


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