Question Numbers (1 to 5): Every day a widget supplier supplies widgets from the warehouse (W) to four locations – Ahmednagar (A), Bikrampore (B), Chitrachak (C), and Deccan Park (D). The daily demand for widgets in each location is uncertain and independent of each other. Demands and corresponding probability values (in parenthesis) are given against each location (A, B, C, and D) in the figure below. For example, there is a 40% chance that the demand in Ahmednagar will be 50 units and a 60% chance that the demand will be 70 units. The lines in the figure connecting the locations and warehouse represent two-way roads connecting those places with the distances (in km) shown beside the line. The distances in both the directions along a road are equal. For example, the road from Ahmednagar to Bikrampore and the road from Bikrampore to Ahmednagar are both 6 km long.

Every day the supplier gets the information about the demand values of the four locations and creates the travel route that starts from the warehouse and ends at a location after visiting all the locations exactly once. While making the route plan, the supplier goes to the locations in decreasing order of demand. If there is a tie for the choice of the next location, the supplier will go to the location closest to the current location. Also, while creating the route, the supplier can either follow the direct path (if available) from one location to another or can take the path via the warehouse. If both paths are available (direct and via warehouse), the supplier will choose the path with minimum distance.

Question 1- If the last location visited is Ahmednagar, then what is the total distance covered in the route (in km)?

Explanation

Correct answer- 35

Given that the last location is Ahmednagar, which means that the demand at A was the least among the four locations.

So the demand at A is 50. Then demand at B will be 60 and demand at D will be 50 (because these values cannot be less than the demand at A). Demand at C can be either 70 or 100, whichever be the case he will go from the warehouse to C first, thereby c traveling 12 km. From C he will go the the location with the next highest demand, which is B, thereby covering 4 km. Then he will go to D and cover (10 + 2 =) 12 km. Finally he will go to A, taking the path with the least distance, thereby covering (2 + 5 =) 7 km.

Total distance covered = 12 + 4 + 12 + 7 = 35 km.

Question 2-

 If the total number of widgets delivered in a day is 250 units, then what is the total distance covered in the route (in km)?

Explanation

Correct answer- 38

Given that the total number of widgets delivered is 250. The maximum possible number of widgets delivered can be 280 and the minimum possible number is 190. Note that 250 is 30 less than 280. Also the minimum and maximum demand in three out of four locations differ by 20 whereas in C it differs by 30. So the only possible way in which 250 widgets are delivered is:

A(70), B(6), C(70) and D(50). The first location visited is A, then C, Third is B and last location is D.

Distance covered = 5 + 5 + 12 + 4 + 10 + 2 = 38 km.

Question 3-

What is the chance that the total number of widgets delivered in a day is 260 units and the route ends at Bikrampore?

1)  7.56%

2)  33.33%

3)  10.80%

4)  17.64%

Explanation

Correct answer- 1

Question -4

 If the first location visited from the warehouse is Ahmednagar, then what is the chance that the total distance covered in the route is 40 km?

1)  30%

2)  3.24%

3)  18%

4)  5.4%

Explanation

Correct answer – 3

Question – 5

If Ahmednagar is not the first location to be visited in a route and the total route distance is 29 km, then which of the following is a possible number of widgets delivered on that day?

1)  220

2)  250

3)  200

4)  210

Explanation

Correct answer- 4

Given that A is not the first location to be visited, this means that C is definitely visited first. The only route that will have a total distance of 29 km is C-B-A-D. The demand at C may be 100 or 70, at B it is 60, at A it is 50 and at D it may be 30 or 50. The total distance covered is 12 + 4 + 6 + 5 + 2 = 29 km. So the total number of widgets delivered can be 210, 230, 240 or 260.
Hence, 210 is a possible number of widgets that was delivered on that day.