# not getting the right proportion

I got this answer wrong. I thought it was 55% but it seems the answer is different. Please can you have a look at this and tell me where have I gone wrong and it should be. Thanks in advance.

Q) Approximately what proportion of the total number of seats in all Buses and Trains are empty?

EDITED - I FORGOT TO INCLUDE MULTPLY CHOICES

A) 45% B) 50% C) 55% D) 60% E) 65%

*Assume For Buses*
Average No of Vehicles per Day (000's) = 112
Average Distance Travelled by one Vehicle per Day (km) = 57
Average No of Seats = 55
Average Occupancy (%) = 57

*Assume For Trains*
Average No of Vehicles per Day (000's) = 89
Average Distance Travelled by one Vehicle per Day (km) = 108
Average No of Seats = 430
Average Occupancy (%) = 44


The steps I took are the following...

 Step 1- Find total seats for Buses and Trains == 55 + 430 = 485
Step 2 - Find number of empty seats for Buses == 100 - 57 = 43.
55 * 0.43 = 23.65
Step 3 - Find number of empty seats for Trains == 100 - 44 = 56.
430 * 0.56 = 240.8
Step 4 - 23.65 + 240.8 = 264.45.
Step 5 - 264.45 / 485 = 0.5452 * 100 = **55%**


EDITED STILL NOT GETTING THIS RIGHT

2nd attempt

for buses
112000 * 55 / 112000 * 43 = 616000 / 48160000 = 0.127906976
for trains
89000 * 430 / 89000 * 56 = 38270000 / 4984000 = 0.76785714

0.127906976 + 0.76785714 / 485  = 7.806478405/ 485 = 0.016095831  < this is wrong


3rd attempt

for buses
112000 * 55 / 112000 * 0.43 = 616000 / 48160 = 12.79069767
for trains
89000 * 430 / 89000 * 0.56 = 38270000 / 49840 = 76.78571429

12.79069767 + 76.78571429 = 89.57641196 / 485 = 0.184693632  < this is wrong

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You lost a zero in the numerator for buses, it should be 6160000. You should not divide by the 112000 then, and the 0.43 goes in the numerator, not the denominator. Generally when you use a slash for division, it is important to parenthesize afterward to avoid confusion. –  Ross Millikan Nov 21 '11 at 14:45

## 1 Answer

You need to find the total number of seats on all the buses by multiplying the number of buses by the seats/bus then the number of vacant bus seats using the percentage. Then similarly for trains. Your calculation would be correct if there is only one bus and only one train. The fact that there are many more buses makes the bus occupancy be weighted much higher than train occupancy.

Added: You should not be dividing by the number of buses or trains. The number of empty bus seats is 112000 * 55 * 0.43= 2,648,800. The number of empty train seats is 89000 * 430 * .56=21,431,200\$ The proportion of empty seats is (112000 * 55 * 0.43 + 89000 * 430 * .56)/(112000 * 55 + 89000 * 430 )=0.542

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"multiplying the number of buses by the seats/bus then the number of vacant bus seats using the percentage" is that multiplying the number of buses by the seats divided by the number of vacant bus seats using the percentage. –  DiscoDude Nov 20 '11 at 23:38
Right. 112000 buses * 55 seats/bus *43% vacant = empty bus seats. Your overall vacancy is (empty bus seats+empty train seats)/(total bus seats + total train seats) –  Ross Millikan Nov 20 '11 at 23:40
I have edited the above calculation and I am not getting it right.If you can have a look, most appericated but I will still continue to work on it. –  DiscoDude Nov 21 '11 at 14:32
pls accept my apologies I forgot to include the multiple choices. The answer you have provided seems to be either 55% or 50% (to the nearest choice I have) which in that case when I did the question again the answer was wrong. However if I do 100 - 54.2 = 45, I believe the answer maybe correct. I will update soon. –  DiscoDude Nov 21 '11 at 17:38
54.2% is not far from 55%. I would pick that one. –  Ross Millikan Nov 21 '11 at 17:40