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Q.

A batch of bottles were packed in 25 boxes with 12 bottles in each box. If the same batch is packed using 20 bottles in each box, then the number boxes would be:


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a

12

b

13

c

14

d

15 

answer is D.

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Detailed Solution

Given that,
If there are 25 boxes, then the number of bottles in each box = 12.
Here, we have to find the number of boxes if there are 20 bottles in each box.
We know that two variables are said to be inversely proportional if and only if they are directly proportional to one another's reciprocal. If x and y   are two variables in inverse variations, then
xy=k,   where k is a proportionality constant.
If the no. of bottles in each box increases, no. of boxes will decrease.
Hence, it is inverse proportion.
Then from the given data, we can draw the following table as,

Number of boxes (x)  

Number of bottles in each box (y)  

x 1 =25  

y 1 =12  

x 2  

y 2 =20  

Using the relation of inverse proportion x 1 y 1 = x 2 y 2  , we get,
x 1 y 1 = x 2 y 2     ⇒ x 2 = x 1 y 1 y 2 ⇒ x 2 = 25×12 20  
∴ x 2 =15    Therefore, there are 15 such boxes.
Hence, option 4 is correct.
 
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