Passengers on a Bus- DI set
Ms Voyager was on her solo trip to Shimla. She boarded the local passenger bus called “Traveller” from “Summer Hill (SH)” stop and got off at “Old Shimla” (OS)”. In between there are five stations and she decided to take a note of the number of passengers who boarded and got off “Traveller”.
Also the price of ticket between two stations is equal to one plus the number of stations in between those two stations. For example the ticket price of one passenger from Summer Hill to the mall road is equal to Rs 3 and that of one passenger from Monkey Point to Old Shimla is Rs 5. When she got off the Traveller at Old Shimla Bus stand she had following information with her. Also no person got off the same stop at which he/she boarded.
Route of Traveller
1. Summer Hill (SH) – First stop
2. Monkey Point(MP)
3. Railway station(RS)
4. The mall Road(MR)
5. Ridge(RD)
6. Jakhu temple(JT)
7. Old Shimla – Last stop
All the remaining passengers got off the bus at the last stop. Ms Voyager is also one of the passengers only.
Q 1) What could be the maximum revenue of tickets bought from Summer Hill to Old Shimla?
a) 55
b) 66
c) 44
d) 77
Solution:
For maximum revenue, we need to maximize the number of people who travelled from Summer Hill to Old Shimla. To maximize the number we need to make sure that out of 16 people who got on at Summer Hill least number of people get off at stops other than Old Shimla. So out of 16 from Summer Hill, 8 will definitely get off at MP. Then out of 14 people getting off at RS at least 3 must be from SH because at max 11 can be from MP. There after at every stop all the passengers can be arranged to have got on at stations other than SH.
So the required number is 16-8-3 = 5. Also Ms Voyager got off at OS only. So the required number becomes 6. So the revenue becomes 6*11 = 66 Rs.
Q2) What could be the maximum revenue of tickets bought from RS to RD?
a) 26 Rs
b) 28 Rs
c) 18 Rs
d) 22 Rs
Solution:
Before RS, a total of 27(16+11) people have boarded the Traveller and 22(8+14) have gotten off from it. So before RS there are already 5 people sitting inside Traveller. Now at RS, 15 more people get on.so a total of 20 people are sitting on Traveller right now. 9 get off at MR. so we can say that at least 4 people who got on at RS must have gotten off at MR. So the remaining 11 people who got on at RS got off at RD. so the revenue would be 11*2 = 22 Rs.
Q3) At most how many passengers who got on the Traveller at any stop got off at immediately next stop?
a) 69
b) 65
c) 63
d) 59
Solution: Of 16 passengers who got on at SH, Max 8 can get off at MP. Of 11 who got on at MP, all 11 can get off at RS. Out of 15 who got on at RS, max 9 can get off at MR. similarly, of 16 at MR, all 16 can get off at RD. of 18 form RD, 13 can get off at JT and all 8 out of 8 from JT can get off at OS.
So the required number is 8+11+9+16+13+8 = 65.
Q4) At most how many passengers who got on at any stop got off at the 3rd stop after that?
a) 12
b) 17
c) 15
d) 18
Solution: The pair of stops that qualify for this question are :
SH – MR
MP – RD
RS – JT
MR – OS
The maximum number of passengers from SH to MR = 5.
The maximum number of passengers from MP to RD = 0.
The maximum number of passengers from RS to JD = 10.
The maximum number of passengers from MR to OS = 0.
So the required number is 15.
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