Question

Akshay has completely put each of three liquids, 558 liters of petrol, 682 liters of diesel and 589 liters of kerosene in bottles of equal size without mixing any of the above three types of liquids such that each bottle is completely filled. What is the least possible number of bottles required?

• A. \(56 \)
• B. \(59 \)
• C. \(63 \)
• D. \(66 \)
• E. \(60 \)

Hint:

For minimum number of containers: - Use HCF of given quantities as container size - Then divide each quantity and add the results

Answer 1

The Correct Option is D

Concept: To minimize the number of bottles, we must maximize the size of each bottle. Thus, we find the HCF of the given quantities.
• Bottle size = HCF of all quantities
• Number of bottles = Total quantity $\div$ bottle size
Step 1: Find HCF of 558, 682, and 589.
Prime factorization: \[ 558 = 2 \times 3^2 \times 31 \] \[ 682 = 2 \times 11 \times 31 \] \[ 589 = 19 \times 31 \] Common factor: \[ \text{HCF} = 31 \]

Step 2: Find number of bottles.
\[ \frac{558}{31} = 18, \quad \frac{682}{31} = 22, \quad \frac{589}{31} = 19 \] \[ \text{Total bottles} = 18 + 22 + 19 = 59 \]