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Question

The digits of a three digit number are in the ratio 1:2:3. If the units digit and the hundreds digit are interchanged with each other, then the number becomes 396 more than the original number. Find the number.
  1. 123
  2. 246
  3. 642
  4. 369


Solution

The correct option is B 246
Let the digits of the three digitnumber be x, 2x, 3x.

So, the number is, (100×x)+(10×2x)+3x=123x

After interchaning the units digit andthe hundreds digit, the number becomes (100×3x)+(10×2x)+x=321x.

When the units digit and the hundreds digit are interchanged with each other, we get 321x123x=396198x=396x=396198x=2

Therefore, the digits are x=2,2x=4 and 3x=6

Thus, the number =123x=123×2=246.

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