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.

• A. 123
• B. 246
• C. 642
• D. 369

Answer 1

The correct option is B 246

$\text{Let the digits of the three digit}\text{number be x, 2x, 3x.}$

$\text{So, the number is,}(100\times x)+(10\times 2x)+3x=123x$

$\text{After interchaning the units digit and}\text{the hundreds digit, the number}\text{becomes}(100\times 3x)+(10\times 2x)+x=321x.$

$\text{When the units digit and the}\text{hundreds digit are interchanged with}\text{each other, we get}321x-123x=396\Rightarrow 198x=396\Rightarrow x=\frac{396}{198}\Rightarrow x=2$

$\text{Therefore, the digits are}x=2,2x=4\text{and}3x=6$

$\text{Thus, the number}=123x=123\times 2=246.$