The difference between a two-digit number and the number obtained by interchanging the two digits of the number is 9. The sum of the two digits of the number is 15. What is the product of the two digits of the two digit number?
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............... Here it is
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Let the unit digit be x and ten's digit be y .
So, Number will be 10y + x .
After, reversing the digits, number = 10x +y.
Now,
As per the question,
10y+x - (10x+y ) = 9
=> 10y + x -10x - y = 9
=> 9y-9x = 9
=> 9(y-x) = 9
=> y- x = 1......(i)
Again,
x+ y = 15.......(ii)
By solving (i) and (ii) ,
2y = 16, y = 8.
And, x = 7.
Thus, Number will be 87.
And, product of the digits will be 56.
So, Number will be 10y + x .
After, reversing the digits, number = 10x +y.
Now,
As per the question,
10y+x - (10x+y ) = 9
=> 10y + x -10x - y = 9
=> 9y-9x = 9
=> 9(y-x) = 9
=> y- x = 1......(i)
Again,
x+ y = 15.......(ii)
By solving (i) and (ii) ,
2y = 16, y = 8.
And, x = 7.
Thus, Number will be 87.
And, product of the digits will be 56.
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