Question

A drink vendor has 80 liters of Maaza, 144 liters of Pepsi and 368 liters of Sprint. He wants to pack them in cans so that each can contains the same number of liters of a drink and does not want to mix any two drinks in a can. What is the least number of cons?
A 37
B 48
C 22
D 11

Answer 1

Hint: Each drink should pack in the least number of cans, thus each can should contain the maximum possible liters of the drink. First, we have to find the greatest common factor for 80, 144 and 368. Then we have to divide each of the numbers with the greatest common factor to find the number of cans. After that we have to add all the number of cans to find the required least number of cans used to pack the drinks.

Complete step-by-step answer:
Now, find the greatest common factor.
$\begin{array}{c}80 = 2 \times 2 \times 2 \times 2 \times 5\\144 = 2 \times 2 \times 2 \times 2 \times 3 \times 3\\368 = 2 \times 2 \times 2 \times 2 \times 23\end{array}$

The greatest common factors of 80, 144 and 368 is $2 \times 2 \times 2 \times 2 = 16$

Now, we can find the number of cans used in each drink.
Number of can used to pack Maaza $\begin{array}{c} = \dfrac{{80}}{{16}}\\ = 5\end{array}$

Number of can used to pack Pepsi $\begin{array}{c} = \dfrac{{144}}{{16}}\\ = 9\end{array}$

Number of can used to pack Sprite $\begin{array}{c} = \dfrac{{368}}{{16}}\\ = 23\end{array}$

Now, we have to calculate the total number of cans by adding all the numbers of cans used to pack each of the drinks.
Required numbers of can $\begin{array}{c} = 5 + 9 + 23\\ = 37\end{array}$

Hence, the correct option is A.

Note: We have to determine the least number of cans required for a given case. Since, the amount of each drink is given, thus we have to find the greatest common factor which is 16. With the help of the greatest common factor, we can find the number of cans.