Question

A milkman has milk of three varieties. He has 403L, 465L & 651L of the three varieties of milk with him. 1. What is the largest size of bottle in which he can bottle each of the three types of milk completely without mixing the milk? 2. What is the minimum number of bottles required? 3. How many different sizes of bottles (with the integral number of litres) can be used in order to bottle all three varieties of milk? (write comma-separated integers with spaces, eg: x, y, z)​

Answer 1

Step-by-step explanation:

This is the answer.

Answer. a) The largest size of bottle in which he can bottle each of the three types of milk completely without mixing the milk :- 31 L

Use HCF method and 31 will divide all three numbers and it is a prime number

b) What is the minimum no:of bottles required:-

let a bottle size be 'b'

Minimum no:of bottle required = 403/b + 465/b + 651/b

To minimize this equation 'b' should be maximized

So maximum value of b= 31

Thus minimum number of bottle required

= 403/31 + 465/31 + 651/31 = 13+15+21 = 49 L

c) This part is asking about how many factors do 31 have so , 31 has two factors 31, 1.

Hence 2 size of bottle can be used.

Hope that my explanation will help you to understand this questions answer.

Answer 2

Answer:

a)Three varieties of milk are 402L, 465L & 651L.

The largest bottle size means HCF of these numbers.

Step1: Find the smallest difference between all the pairs of numbers. So, the smallest difference comes out between 465 & 403, which is 62, as all other differences are greater than 62.

Step2: Factors of 62 are

                           1x62

                           2x31

31 is a Prime number so no further factor is possible.

62->Does Not divide 403. 31 will divide all the three numbers.

Thus, the largest bottle size is 31L.

b) Let a bottle size of ‘b’ L.

Minimum No. of bottle required = 403/b + 465/b +651/b  ………(1)

To minimize this equation ‘b’ should be maximized. So, the maximum value of b = 31L.

Thus,

           Minimum no. of bottle required = 403/31 + 465/31 + 651/31

                                                            = 13+15+21

                                                            = 49L.

c) This part is basically asking how many factors 31 has. Since 31 is a prime number, so, it has only two factors 31 & 1. Hence, 2 sizes of bottles can be used.

Step-by-step explanation: