A can X contains 399 litres of petrol and a can Y contains 532 litres of diesel. They are to be bottled in bottles of equal size so that whole of petrol and diesel would be separately bottled. The bottle capacity in terms of litres is an integer. How many different bottle sizes are possible?
Answer & explanation
Answer: (b) 4
A bottle size must divide both 399 and 532 exactly, i.e. it must divide their HCF, 133 = 7 × 19. The number 133 has four divisors: 1, 7, 19 and 133.
- 399 = 3 × 7 × 19 and 532 = 2² × 7 × 19.
- HCF(399, 532) = 7 × 19 = 133.
- Every common divisor divides 133: 1, 7, 19 and 133.
- So 4 different bottle sizes are possible.
- Check: 532 − 399 = 133, and 399 = 3 × 133, 532 = 4 × 133.
Remember · ‘Equal bottles for both’ means common divisors; their number equals the number of divisors of the HCF.
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). ·