What is the number of fives used in numbering a 260-page book?

Answer: (b) 56

Count the digit 5 place by place in 1 to 260. It appears 26 times in the units place and 30 times in the tens place (50–59, 150–159, 250–259), a total of 56.

1. Units place: 5, 15, 25, …, 255, which is 26 numbers.
2. Tens place: 50–59, 150–159 and 250–259, 10 each, 30 in all.
3. Hundreds place: there is no page from 500 upwards, so 0.
4. Total fives = 26 + 30 = 56.
5. Check: 55, 155 and 255 each use two fives; they are counted once in the units count and once in the tens count, as they should be.

Remember · Count a digit place by place (units, tens, hundreds); numbers like 55 are then automatically counted twice.

Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). · Report an error