A 3-digit number is such that the units' digit, the tens' digit, and the hundreds' digit are in the ratio 1 : 2 : 3. The sum of this number and the number obtained by writing its digits in reverse order is 1332. Find the number.
963
The correct answer is Option 1 i.e. 963.
Let the three-digit number be abc
Ratio of digits = 1 : 2 : 3 (units : tens : hundreds)
so,
⇒ a = 3x, b = 2x, c = x
The number = abc = 100a + 10b + c
⇒ 100 × 3x + 10 × 2x + x = 300x + 20x + x = 321x
The number obtained by reversing the digits = cba
⇒ 100c + 10b + a
⇒ 100 × x + 10 × 2x + 3x = 123x
⇒ 321x + 123x = 1332
⇒ 444x = 1332
⇒ x = 3
Thus, a = 9, b = 6, and c = 3
Thus, the number is: 963
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