in a three digit number units digit tens digit and hundred digit are in the ratio 3 : 5 : 7 if the difference of original number and the number obtained by reversing the digit is 396 find the number
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Answer:
-357
Step-by-step explanation:
Unit digit : Tens Digit : Hundred digit ::: 3:5:7
let say unit digit = 3x
then tens digit = 5x
Hundred digit = 7x
7x would be any number between 0 to 9
so only possible value of x = 1 or -1
so unit digit = 3 or -3
Tens Digit = 5 or -5
Hundred digit = 7 or - 7
so number = 357 or -357
case 1
Number = 357
interchanges number = 753
so 357 - 753 = - 396 ( not equal to 396)
Case2
Number = -357
interchanged number = -753
so -357 - (-753) = 396
Another way to solve
say number = xyz
interchanged number = zyx
xyz = 100x + 10y + z
zyx = 100z + 10y + x
xyz - zyx = 396
100x + 10y + z - 100z - 10y - x = 396
99x - 99z = 396
x - z = 4
x/z = 3/7
x = 3z/7
3z/7 - z = 4
3z - 7z = 28
-4z = 28
z = -7
x = -3
y = -5 ( as y/z = 5/7)
number = -357
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