A train ‘T’ starts from station ‘A’ for station ‘F’. In between stations ‘A’ and ‘F’, there are four intermediate stations ‘B’, ‘C’, ‘D’ and ‘E’, respectively, in the same order. Stations ‘A’, ‘B’, ‘C’, ‘D’ and ‘E’ has quota for seats booking. The line graph given below represents the percentage distribution of quota of seats given to the respective stations out of total number of seats in the train and percentage of seats booked out of them.
The table below represents the total vacant seats in the train after leaving the respective stations.
| Stations | Total vacant seats |
| B | 562 |
| C | 494 |
| D | 514 |
| E | 472 |
Note:
1. When train left station A, number of vacant seats was 688 and 30% of quota seats of station A were not booked.
2. A seat can be booked for only one person from the respective stations and the same person can board the train from that station.
3. All the persons who booked tickets boarded the train.
Find the ratio of number of passengers who boarded the train at station ‘B’ and number of passengers who de-boarded the train at station ‘D’.
- 13:9
- 12:7
- 18:11
- 10:3
The Correct Option is C
Solution and Explanation
The correct option is (C): 18:11.
Let total number of seats in the train be ‘x’
Percentage of quota of seats given to station ‘A’ = 100 – (30 + 25 + 10 +15) = 20%
So, number of seats available for booking in station A = 0.2x
Therefore, number of seats booked station A = 70% of 0.2x = 0.14x
So, x – 688 = 0.14x
Or, 0.86x = 688
Or, x = 688/0.86 = 800
The table below shows the information about number of seats available, booked and not booked for respective stations.
| Station | Number of seats which is available for booking | Number of seats which were booked | Number of seats which were not booked |
| A | 20% of 800 = 160 | 70% of 160 =112 | 48 |
| B | 30% of 800 = 240 | 60% of 240 =144 | 96 |
| C | 25% of 800 = 200 | 55% of 200 =110 | 90 |
| D | 10% of 800 = 80 | 85% of 80 = 68 | 12 |
| E | 15% of 800 = 120 | 65% of 120 =78 | 42 |
So, number of passengers in the train after leaving station ‘B’ = 800 –562 = 238
Number of passengers who boarded from station ‘A’ = 112
Number of passengers who boarded from station ‘B’ = 144
Therefore, number of passengers in the train after leaving station ‘B’ =Number of passengers who boarded from station ‘A’ + Number of
passengers who boarded from station ‘B’ – number of passengers who de-boarded at station ‘B’
So, 238 = 112 + 144 – number of passengers who de-boarded at station ‘B’
Or, number of passengers who de-boarded at station ‘B’ = 256 – 238 =18
Similarly,
| Station | Number of seats which is available for booking | Number of seats which were booked | Number of seats which were not booked |
| A | 112 | 112 | - |
| B | 144 | 238 | 18 |
| C | 110 | 306 | 42 |
| D | 68 | 286 | 88 |
| E | 78 | 328 | 36 |
| F | - | - | 328 |
Required ratio = 144:88 = 18:11.
boarded at station ‘B’
So, 238 = 112 + 144 – number of passengers who de-boarded at station ‘B’
Or, number of passengers who de-boarded at station ‘B’ = 256 – 238 =18
Similarly,
| Station | Number of seats which is available for booking | Number of seats which were booked | Number of seats which were not booked |
| A | 112 | 112 | - |
| B | 144 | 238 | 18 |
| C | 110 | 306 | 42 |
| D | 68 | 286 | 88 |
| E | 78 | 328 | 36 |
| F | - | - | 328 |
Required ratio = 144:88 = 18:11.
Out of total number of passengers in the train after it left station ‘C’, 50% were females. Find the difference between number of males in the train after it left station ‘C’ and number of passengers who deboarded the train at station ‘B’.
- 135
- 215
- 123
- 141
The Correct Option is A
Solution and Explanation
The correct option is (A): 135.
Let total number of seats in the train be ‘x’
Percentage of quota of seats given to station ‘A’ = 100 – (30 + 25 + 10 +15) = 20%
So, number of seats available for booking in station A = 0.2x
Therefore, number of seats booked station A = 70% of 0.2x = 0.14x
So, x – 688 = 0.14x
Or, 0.86x = 688
Or, x = \(\frac{688}{0.86} \)= 800
The table below shows the information about number of seats available, booked and not booked for respective stations.
| Station | Number of seats which is available for booking | Number of seats which were booked | Number of seats which were not booked |
| A | 20% of 800 = 160 | 70% of 160 =112 | 48 |
| B | 30% of 800 = 240 | 60% of 240 =144 | 96 |
| C | 25% of 800 = 200 | 55% of 200 =110 | 90 |
| D | 10% of 800 = 80 | 85% of 80 = 68 | 12 |
| E | 15% of 800 = 120 | 65% of 120 =78 | 42 |
So, number of passengers in the train after leaving station ‘B’ = 800 –562 = 238
Number of passengers who boarded from station ‘A’ = 112
Number of passengers who boarded from station ‘B’ = 144
Therefore, number of passengers in the train after leaving station ‘B’ =Number of passengers who boarded from station ‘A’ + Number of
passengers who boarded from station ‘B’ – number of passengers who de-boarded at station ‘B’
So, 238 = 112 + 144 – number of passengers who de-boarded at station ‘B’
Or, number of passengers who de-boarded at station ‘B’ = 256 – 238 =18
Similarly,
| Station | Number of seats which is available for booking | Number of seats which were booked | Number of seats which were not booked |
| A | 112 | 112 | - |
| B | 144 | 238 | 18 |
| C | 110 | 306 | 42 |
| D | 68 | 286 | 88 |
| E | 78 | 328 | 36 |
| F | - | - | 328 |
Required difference = (0.5 × 306) – 18 = 153 – 18 = 135.
rded at station ‘B’
So, 238 = 112 + 144 – number of passengers who de-boarded at station ‘B’
Or, number of passengers who de-boarded at station ‘B’ = 256 – 238 =18
Similarly,
| Station | Number of seats which is available for booking | Number of seats which were booked | Number of seats which were not booked |
| A | 112 | 112 | - |
| B | 144 | 238 | 18 |
| C | 110 | 306 | 42 |
| D | 68 | 286 | 88 |
| E | 78 | 328 | 36 |
| F | - | - | 328 |
Required difference = (0.5 × 306) – 18 = 153 – 18 = 135.
Find the average of the number of passengers who de-boarded the train at stations ‘E’ and ‘F’ together.
- 212
- 272
- 192
- 182
The Correct Option is D
Solution and Explanation
The correct option is (D): 182.
Let total number of seats in the train be ‘x’
Percentage of quota of seats given to station ‘A’ = 100 – (30 + 25 + 10 +15) = 20%
So, number of seats available for booking in station A = 0.2x
Therefore, number of seats booked station A = 70% of 0.2x = 0.14x
So, x – 688 = 0.14x
Or, 0.86x = 688
Or, x = 688/0.86 = 800
The table below shows the information about number of seats available, booked and not booked for respective stations.
| Station | Number of seats which is available for booking | Number of seats which were booked | Number of seats which were not booked |
| A | 20% of 800 = 160 | 70% of 160 =112 | 48 |
| B | 30% of 800 = 240 | 60% of 240 =144 | 96 |
| C | 25% of 800 = 200 | 55% of 200 =110 | 90 |
| D | 10% of 800 = 80 | 85% of 80 = 68 | 12 |
| E | 15% of 800 = 120 | 65% of 120 =78 | 42 |
So, number of passengers in the train after leaving station ‘B’ = 800 –562 = 238
Number of passengers who boarded from station ‘A’ = 112
Number of passengers who boarded from station ‘B’ = 144
Therefore, number of passengers in the train after leaving station ‘B’ =Number of passengers who boarded from station ‘A’ + Number of
passengers who boarded from station ‘B’ – number of passengers who de-boarded at station ‘B’
So, 238 = 112 + 144 – number of passengers who de-boarded at station ‘B’
Or, number of passengers who de-boarded at station ‘B’ = 256 – 238 =18
Similarly,
| Station | Number of seats which is available for booking | Number of seats which were booked | Number of seats which were not booked |
| A | 112 | 112 | - |
| B | 144 | 238 | 18 |
| C | 110 | 306 | 42 |
| D | 68 | 286 | 88 |
| E | 78 | 328 | 36 |
| F | - | - | 328 |
Required average = {\(\frac{(36 + 328)}{2}\)} = 182.
After the train left station ‘D’, each passenger has 3 bags with him.
Find the total number of bags with the passengers in the train after it left
station ‘D’.
Find the total number of bags with the passengers in the train after it left
station ‘D’.
- 766
- 512
- 858
- 912
The Correct Option is C
Solution and Explanation
The correct option is (C): 858.
Let total number of seats in the train be ‘x’
Percentage of quota of seats given to station ‘A’ = 100 – (30 + 25 + 10 +15) = 20%
So, number of seats available for booking in station A = 0.2x
Therefore, number of seats booked station A = 70% of 0.2x = 0.14x
So, x – 688 = 0.14x
Or, 0.86x = 688
Or, x = 688/0.86 = 800
The table below shows the information about number of seats available, booked and not booked for respective stations.
| Station | Number of seats which is available for booking | Number of seats which were booked | Number of seats which were not booked |
| A | 20% of 800 = 160 | 70% of 160 =112 | 48 |
| B | 30% of 800 = 240 | 60% of 240 =144 | 96 |
| C | 25% of 800 = 200 | 55% of 200 =110 | 90 |
| D | 10% of 800 = 80 | 85% of 80 = 68 | 12 |
| E | 15% of 800 = 120 | 65% of 120 =78 | 42 |
So, number of passengers in the train after leaving station ‘B’ = 800 –562 = 238
Number of passengers who boarded from station ‘A’ = 112
Number of passengers who boarded from station ‘B’ = 144
Therefore, number of passengers in the train after leaving station ‘B’ =Number of passengers who boarded from station ‘A’ + Number of
passengers who boarded from station ‘B’ – number of passengers who de-boarded at station ‘B’
So, 238 = 112 + 144 – number of passengers who de-boarded at station ‘B’
Or, number of passengers who de-boarded at station ‘B’ = 256 – 238 =18
Similarly,
| Station | Number of seats which is available for booking | Number of seats which were booked | Number of seats which were not booked |
| A | 112 | 112 | - |
| B | 144 | 238 | 18 |
| C | 110 | 306 | 42 |
| D | 68 | 286 | 88 |
| E | 78 | 328 | 36 |
| F | - | - | 328 |
Required number of bags = 286 × 3 = 858.
If at each station, 75% of total number of passengers who boarded the train were males then find the sum of number of all the females who boarded the train at given stations.
- 194
- 148
- 156
- 128
The Correct Option is D
Solution and Explanation
The correct option is (D): 128.
Let total number of seats in the train be ‘x’
Percentage of quota of seats given to station ‘A’ = 100 – (30 + 25 + 10 +15) = 20%
So, number of seats available for booking in station A = 0.2x
Therefore, number of seats booked station A = 70% of 0.2x = 0.14x
So, x – 688 = 0.14x
Or, 0.86x = 688
Or, x = 688/0.86 = 800
The table below shows the information about number of seats available, booked and not booked for respective stations.
| Station | Number of seats which is available for booking | Number of seats which were booked | Number of seats which were not booked |
| A | 20% of 800 = 160 | 70% of 160 =112 | 48 |
| B | 30% of 800 = 240 | 60% of 240 =144 | 96 |
| C | 25% of 800 = 200 | 55% of 200 =110 | 90 |
| D | 10% of 800 = 80 | 85% of 80 = 68 | 12 |
| E | 15% of 800 = 120 | 65% of 120 =78 | 42 |
So, number of passengers in the train after leaving station ‘B’ = 800 –562 = 238
Number of passengers who boarded from station ‘A’ = 112
Number of passengers who boarded from station ‘B’ = 144
Therefore, number of passengers in the train after leaving station ‘B’ =Number of passengers who boarded from station ‘A’ + Number of
passengers who boarded from station ‘B’ – number of passengers who de-boarded at station ‘B’
So, 238 = 112 + 144 – number of passengers who de-boarded at station ‘B’
Or, number of passengers who de-boarded at station ‘B’ = 256 – 238 =18
Similarly,
| Station | Number of seats which is available for booking | Number of seats which were booked | Number of seats which were not booked |
| A | 112 | 112 | - |
| B | 144 | 238 | 18 |
| C | 110 | 306 | 42 |
| D | 68 | 286 | 88 |
| E | 78 | 328 | 36 |
| F | - | - | 328 |
Required number of females = 0.25 × (112 + 144 + 110 + 68 + 78) =128.
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