Question

A shopkeeper has 50 cold drink bottles. Some of the bottles are 1-liter and some are 2- liter bottles. The average cold drink of the bottles is 1200 ml . Find the number of 2-liter bottles. (1 liter = 1000 ml)

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Answer 1

Answer:

We have two groups, one of 1-lit bottles and other one of 2-lit bottles. Let us say number of 2-lit bottles is N1 and number of 2-lit bottles is N2. We know that N1 + N2 = 50 as given the in question. The average of group 1 (W1) is 1000 ml as all the bottles are of equal quantity, i.e. 1000 ml. Similarly, the average of group 2 (W2) is 2000 ml. With the help of weighted average formula we can calculate N1 and N2. The weighted average here is 1200 ml. Let us put the values in the equation.

$1200 = \dfrac{N1 x 1000 + N2 x 2000}{N1 + N2}$

As N1 + N2 = 50, Replacing and solving for N1 we get, N1 = 40 and N2 = 10. Thus, the shopkeeper has 10 bottles of 2-lit.

Answer 2

Answer:

The number of 2-liter bottles = 10

Given :

• Total number of cold drink bottles = 50
• the volume of some bottles = 1 liter
• The volume of other bottles = 2 liters
• The average volume of all the cold drink bottles = 1200ml

TO FIND :

• Total number of 2-liter bottles

SOLUTION:

We can simply solve the problem as under:

LET, Total number of 1-liter bottles = n1

Total number of 2-liter bottles = n2

WE KNOW THAT The Total Number Of Bottles;

n1+ n2 = 50

The average volume of n1, w1 = 1000 ml ( since each bottle has equal amount of cold drink )

similarly, Average volume of n2, w1 = 2000 ml.

Now, APPLYING THE FORMULA FOR WEIGHTED AVERAGE :

Weighted average = n1w1 + n2w2/n1+n2

putting the values in the above formula we have :

1200 = n1 × 1000 + n2 × 2000/ 50

60000 = 1000n1 + 2000n2

solving for n1 We get, n1 = 40

solving for n2 we get, n2 = 10

so, The total number of 2-liter bottles = 10

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