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:
From the standpoint of the Inspector, what can be the minimum number of private vehicles in the queue, whose registration cannot be processed immediately at that point of time ?
128
117
228
78
Total number of private vehicles in queue = (120*3 + 30) = 390
78 are the lowest number of Sedans whose single verification is complete, in this case verification of filled up Form 20.
96 are the lowest number of Hatchbacks whose single verification is complete, in this case verification of Sales Invoice from dealer.
78 are the lowest number of SUVs whose single verification is complete, in this case verification of Insurance Certificate.
10 is the lowest number of 4x4 Wheelers whose single verification is complete, in this case verification of Identity proof of owner.
Hence, the maximum number of Sedans, Hatchbacks, SUVs and 4x4 Wheelers in the queue whose registration can be processed immediately due to the completion of verification of all the four documents necessary for registration can be 78, 96, 78 and 10 respectively.
Hence, the maximum number of private vehicles in the queue whose registration can be processed immediately due to the completion of verification of all the four documents necessary for registration can be (78+96+78+10) = 262
Hence, from the standpoint of the Inspector, the minimum number of private vehicles in the queue whose registration cannot be processed immediately at that point of time = 390 – 262 = 128