A milk vendor has 75 litres of cow milk, 45 litres of toned milk and 30 litres of full cream milk. These should be placed in different trays such that each tray contains the same quantity of milk and two kinds of milk should not be mixed in a tray. What is the least number of trays required to place all the milk?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 10.
We need to determine the HCF of the quantities of milk.
The HCF will be the maximum quantity of milk that can be placed in each tray without mixing the types of milk.
Using the prime factorization method, we can find the HCF of 75, 45 and 30.
⇒ 75 = 3 × 52
⇒ 45 = 32 × 5
⇒ 30 = 2 × 3 × 5
Hence, the HCF = 3 × 5 = 15
Such that each tray can hold 15 liters of a single type of milk.
Now, we can calculate the number of trays needed
Cow milk = 75/15 = 5
Toned milk = 45/15 = 3
Full cream milk = 30/15 = 2
Total number of trays required = 5 + 3 + 2 = 10 trays