The sum of digits of a two digit number is 9. Also,nine times this number is twice the number obtainedby reversing the order of the digits. Find the number.
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Answered by
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Let the no. =10x +y
Let the reversing no. = 10y+ x
A. T. Q
x + y = 9. _____ eq 1
2( 10x + y) = 9 (10y + x)
20x +2y. =90y + 9x
11x. =88y
x. = 8y
putting it into eq 1
x + y = 9
8 + y = 9
y. = 1
Number = 10x + y
= 10(8) + (1)
= 81
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Answered by
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Heya
_______________________________
Let the two digit number be xy
ACCORDING TO THE QUESTION
x + y = 9 ..... Equation ( i )
And
9 ( 10x + y ) = 2 ( 10y + x )
=>
88x - 11y = 0
y = 8x
Now, put value of y = 8x in equation ( i )
8x + x = 9
9x = 9
x = 1
And y = 8
So, the two digit number is 18
______________________________
verification
ACCORDING TO THE QUESTION
Sum of it's digits is 9
i,e 8 +1 = 9
And
9 times this number is twice the number formed by interchanging it's digits I,e
9 ( 18 ) = 2 ( 81 )
162 = 162
Hence, verified
_______________________________
Let the two digit number be xy
ACCORDING TO THE QUESTION
x + y = 9 ..... Equation ( i )
And
9 ( 10x + y ) = 2 ( 10y + x )
=>
88x - 11y = 0
y = 8x
Now, put value of y = 8x in equation ( i )
8x + x = 9
9x = 9
x = 1
And y = 8
So, the two digit number is 18
______________________________
verification
ACCORDING TO THE QUESTION
Sum of it's digits is 9
i,e 8 +1 = 9
And
9 times this number is twice the number formed by interchanging it's digits I,e
9 ( 18 ) = 2 ( 81 )
162 = 162
Hence, verified
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