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A 3-digit number is such that its units' digit, tens' digit and hundreds' digit are in the ratio 2:3:4. The sum of this number and the number obtained by reversing its digits is 1332. Find the positive difference between the 3-digit number and the number formed by reversing its digit.
594
323
396
414
396
Let digits be 2x, 3x, and 4x. The sum of a 3-digit number and its reverse is 101(a+c). Use this to quickly find x, then calculate the positive difference тИг(100c+10b+a)тИТ(100a+10b+c)тИг.
Ratio of units, tens, and hundreds digits = 2 : 3 : 4. Sum of the number and the number obtained by reversing its digits = 1332.
(100c+10b+a)+(100a+10b+c)=1332
Let digits be 2x, 3x, and 4x. The sum of a 3-digit number and its reverse is 101(a+c). Use this to quickly find x, then calculate the positive difference тИг(100c+10b+a)тИТ(100a+10b+c)тИг.
Confusing the order of the ratio or misinterpreting the digits' positions when forming the reversed number.
Step 1: Assume the digits based on the ratio
Given that the units, tens, and hundreds digits are in the ratio 2:3:4, we can represent the digits as: Units = 2x, Tens = 3x, Hundreds = 4x.
Number=100(4x)+10(3x)+2x=432x
Step 2: Formulate the sum with the reversed number
The number formed by reversing its digits has units digit 4x, tens digit 3x, and hundreds digit 2x. Thus, the reversed number is 234x. The sum of the number and its reverse is given as 1332.
432x+234x=1332тЯ╣666x=1332тЯ╣x=2
Step 3: Determine the 3-digit number
Substitute x=2 back into the digit expressions: Hundreds = 4(2)=8 (Wait, 4├Ч2=8, 3├Ч2=6, 2├Ч2=4, so the number is 864 or if 4,3,2 with x=1 and sum scale: Let's check 666x=1332тЯ╣x=2. So the number is 432├Ч2=864 and reverse is 468. Sum = 864+468=1332.)
N=864,Reverse=468
Step 4: Calculate the positive difference
Find the positive difference between the 3-digit number (864) and the number obtained by reversing its digits (468).
Difference=864тИТ468=396
C is correct because the 3-digit number is 864 and its reverse is 468, giving a positive difference of 864 - 468 = 396, which matches option C.
The difference between a 3-digit number and its reverse is always a multiple of 99, specifically 99(cтИТa), which allows for extremely fast calculation in competitive exams.