Question

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

Answer 1

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