CSAT 2023

Q. D is a 3-digit number such that the ratio of the number to the sum of its digits is least. What is the difference between the digit at the hundred’s place and the digit at the unit’s place of D?

(a) 0
(b) 7
(c) 8
(d) 9
Correct Answer: (c) 8

Question from UPSC Prelims 2023 CSAT

Explanation : 

D is a 3-digit number

To minimize the ratio of a number to the sum of its digits, we need to maximize the sum of the digits and minimize the number itself.

The smallest 3-digit number is 100, but this doesn’t maximize the sum of the digits.

The smallest 3-digit number with the maximum digit sum is 199 (1+9+9=19). This gives us a ratio of 10.47, which is the smallest possible for a 3-digit number.

The difference between the digit at the hundred’s place (1) and the digit at the unit’s place (9) of D is 9-1=8.

So, the correct answer is (c) 8.

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