Question

A drink vendor has 368 liters of Maaza, 80 liters of Pepsi and 144 liters of Sprite. He wants to pack them in cans, so that each can contains the same number of liters of a drink, and doesn't want to mix any two drinks in a can. What is the least number of cans required ?
A) 47
B) 46
C) 37
D) 35

Answer 1

16

Q:

A drink vendor has 80 liters of Mazza, 144 liters of Pepsi, and 368 liters of Sprite. He wants to pack them in cans, so that each can contains the same number of liters of a drink, and doesn't want to mix any two drinks in a can. What is the least number of cans required?

A) 35B) 36C) 37D) 38

Answer:   C) 37 

Explanation:

If we want to pack the drinks in the least number of cans possible, then each can should contain the maximum numbers of liters possible.As each can contains the same number liters of a drink, the number of liters in each can is a comman factor for 80,144 and 368; and it is also the highest such factor, as we need to store the maximum number of liters in each can.

So, the number of liters in each can  = HCF of 80,144 and 368 = 16 liters.

Now, number of cans of Maaza = 80/16 = 5

Number of cans of Pepsi = 144/16 = 9

Number of cans of Sprite = 368/16 = 23

Thus, the total number of cans required = 5 + 9 + 23 = 37 

Answer 2

The Total Number of cans required is 37

c) 37

Explanation:

Given:

1. A drink vendor has 368 litres of Maaza, 80 litres of Pepsi and 144 litres of

  Sprite.

2. Each can contain the same number of litres of a drink.

To find:

The least number of cans required

Solution:

==> According to the condition,

==> Each can contain the same number of Litres of drink

==> To find the HCF of the drink

==> The prime factors of 368

==> 368 ÷ 2 = 184

==> 184 ÷ 2  = 92

==> 92  ÷ 2  = 46

==> 46  ÷ 2  = 23

==> 23 ÷ 23 = 1

==> The prime factors of 368  = 2×2×2×2×23

==> The prime factors of 80

==> 80 ÷ 2 = 40

==> 40 ÷ 2  = 20

==> 20 ÷ 2  = 10

==> 10  ÷ 2  = 5

==>   5 ÷ 5  = 1

==> The prime factors of 368  = 2×2×2×2×5

==> The prime factors of 144

==> 144 ÷ 2 = 72

==>  72 ÷ 2  = 36

==> 36  ÷ 2  = 18

==> 18  ÷ 2  = 9

==>   9 ÷ 3  = 3

==>   3 ÷ 3  = 1

==> The prime factors of 368  = 2×2×2×2×3×3

The HCF of 368,80,144

==> The prime factors of 368  = 2×2×2×2×23

==> The prime factors of 368  = 2×2×2×2×5

==> The prime factors of 368  = 2×2×2×2×3×3

The HCF of 368,80,144 = 2×2×2×2

The HCF of 368,80,144 = 16

No.of cans needed  for 368 litres of Maaza = $\frac{368}{16}$

Number of cans for Mazza = 23

No.of cans needed 80 litres of Pepsi = $\frac{80}{16}$

Number of cans for Pepsi = 5

No.of cans needed 368 litres of Sprite  = $\frac{144}{16}$

Number of cans for Sprite = 9

Total Number of cans required = 23+5+9

The Total Number of cans required is 37

c) 37