UPSC Prelims 2007 Q144: Science & Technology – Quantitative Aptitude
A person has to completely put each of three liquids - 403 litres of petrol, 465 litres of diesel
and 496 litres of mobile oil - in bottles of equal size without mixing any of the three types of
liquids such that each bottle is completely filled. What is the least possible number of bottles
required?
- (a) 34
- (b) 44
- (c) 46
- (d) None of the above
Answer: (b) 44
Explanation
Least number of equal bottles — use the HCF
To use the fewest bottles, each bottle must be as big as possible.
The biggest size that divides all three amounts exactly is their HCF.
Factorise:
| Liquid | Litres | Factors |
|---|---|---|
| Petrol | 403 | 13 × 31 |
| Diesel | 465 | 15 × 31 |
| Mobile oil | 496 | 16 × 31 |
HCF = 31 litres (13, 15 and 16 share no common factor).
Bottles needed: 13 + 15 + 16 = 44.
Answer: (b) 44.
Why each option is right or wrong
- (a) Incorrect. 34 bottles cannot hold all the liquid in equal 31-litre bottles.
- (b) CORRECT. HCF = 31 L → 13 + 15 + 16 = 44 bottles.
- (c) Incorrect. 46 is more than the minimum.
- (d) Incorrect. 44 is among the options.
Key point
Fewest equal containers → bottle size = HCF (31 L). Bottles = 403/31 + 465/31 + 496/31 = 13 + 15 + 16 = 44.
Remember
HCF of the volumes is 31 litres, so 44 bottles.
Common mistakes
- Using the LCM instead of the HCF.
- Not spotting that 31 divides all three numbers.
- Adding the litres and dividing once — liquids cannot be mixed, so divide each separately.
Exam tip
'Largest equal size' or 'fewest containers' → HCF. 'Smallest common multiple' or 'when will they meet again' → LCM.
Sources
- NCERT Class VI — Mathematics, Ch 3 (Playing with Numbers — HCF)
- R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (H.C.F. and L.C.M. of Numbers)