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  • Directions for question : A week before Durga Puja, a Traffic Police Inspector during his beat in front of the Regional Transport Office at Padmapukur, Kolkata, noticed 1

Directions for question :

A week before Durga Puja, a Traffic Police Inspector during his beat in front of the Regional Transport Office at Padmapukur, Kolkata, noticed 120 each of brand new private Sedans, Hatchbacks and SUVs and 30 4x4 Wheelers, which had applied for new registration, queued up along the road in front of the Regional Transport Office in order to get registered. The vehicles and their owners were blocking up a substantial portion of the very busy road for about a kilometer, leading to traffic snarls. 

On enquiry, the manager at the office showed the inspector on his desktop screen a currently updated table showing the data of the individual number of the four necessary documents whose verification has been completed, on all the private vehicles in queue. The manager explained that the time taken up to verify the documents was causing the delay in registration. 

The table on the desktop screen is reproduced below.   

COMPLETED

Sedan

Hatchback

SUV

4x4 Wheelers

Verification of Insurance Certificate

84

102

78

27

Verification of Sales Invoice from dealer

93

96

102

22

Verification of Identity proof of owner

117

111

93

10

Verification of filled up Form 20

78

99

87

29

 

Help the Inspector to analyze the situation at that point of time by answering the following questions using the data from the table, assuming that these four documents mentioned in the table are the only documents needed for registration.

Question:

What can be the maximum number of Hatchbacks in the queue whose verification of exactly one document necessary for registration is completed ?

 

 

Option: 1

24


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

The total number of Hatchbacks is a constant number of 120.

Hence, if we have to maximize the number of Hatchbacks in the queue whose verification of exactly one document is completed, we have to consider as maximum the number of Hatchbacks in the queue whose verification of all the four documents are completed, and all other number of Hatchbacks with a combination of exactly two or exactly three documents with verification completed as minimum, that is zero.

Let x be the number of Hatchbacks in the queue whose verification of exactly one document is complete,

and y be the number of Hatchbacks in the queue whose verification of all the four documents are complete.

Hence, x + y = 120 -------- (equation 1), 

and

x + 4y = (102+96+111+99) = 408 -------- (equation 2)

Subtracting equation 1 from equation 2, we get

3y = 288

or, y = 96

Substituting the value of y in equation 1,

x = 120 – 96 = 24

Hence, the maximum number of Hatchbacks in the queue whose verification of exactly one document necessary for registration is completed may be 24

 

Posted by

Divya Prakash Singh

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