A certain 3-digit code has a zero as its middle digit. The sum of all its digits is 6. If the digits in the hundreds and unit places are swapped, the new number becomes greater than the original by 198. What is the absolute difference between the hundreds and unit digits of the original code?
(a) 6
(b) 3
(c) 4
(d) 2

Question

A certain 3-digit code has a zero as its middle digit. The sum of all its digits is 6. If the digits in the hundreds and unit places are swapped, the new number becomes greater than the original by 198. What is the absolute difference between the hundreds and unit digits of the original code?
(a) 6
(b) 3
(c) 4
(d) 2

ONLiNE UPSC · Accepted Answer

Let number = 100a + 0 + c, so:
a + c = 6
Swapped number = 100c + a
Difference:
100c + a &minus; (100a + c) = 198
99 (c &minus; a) = 198
c &ndash; a = 2 or |a -c| = 2

Hence, option d is correct.

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M Question 1	⏱ 0
A certain 3-digit code has a zero as its middle digit. The sum of all its digits is 6. If the digits in the hundreds and unit places are swapped, the new number becomes greater than the original by 198. What is the absolute difference between the hundreds and unit digits of the original code? (a) 6 (b) 3 (c) 4 (d) 2