Question
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A boat covered a total distance of 2500 km over three days. The ratio of the distance travelled upstream to the distance travelled downstream was 3:2. Over these three days, a total of 3200 passengers travelled on the boat, with the ratio of male to female passengers being 5:3.
On Day 1, the boat travelled 20% of the total upstream distance and 40% of the total downstream distance. On this day, 35% of all male passengers and 50% of all female passengers were on board.
On Day 2, the boat covered 40% of the total upstream distance and 25% of the total downstream distance. The proportion of passengers on this day included 40% of all male passengers and 25% of all female passengers.
Some passengers travelled on multiple days 24 male and 34 female passengers travelled on both Day 1 and Day 2 (excluding Day 3). 20 male and 22 female passengers travelled on both Day 2 and Day 3 (excluding Day 1).16 male and 40 female passengers travelled on both Day 3 and Day 1 (excluding Day 2). 13 male and 9 female passengers travelled on all three days.
Find the ratio between total male passenger on day 2 and 3 together and total female passenger on day 2 and 3 together?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCommon Calculation:
Total distance covered by boat in three days is 2500 km. The ratio of the distance travelled upstream to the distance travelled downstream was 3:2.
Distance covered in upstream is 2500 × 3/ 5 = 1500
Distance covered in downstream is 2500 – 1500 = 1000
The boat travelled 20% of the total upstream distance and 40% of the total downstream distance.
Distance covered in upstream on day 1 is 1500 × 20/100 = 300
Distance covered in downstream on day 1 is 1000 × 40/100=400
The boat covered 40% of the total upstream distance and 25% of the total downstream distance.
Distance covered in upstream on day 2 is 1500 × 40/100 = 600
Distance covered in downstream on day 2 is 1000 × 25/100=250
Distance covered in upstream on day 3 is 1500 – 300 - 600=600
Distance covered in downstream on day 3 is 1000 – 400 – 250 = 350
|
|
Upstream Distance |
Downstream distance |
Total distance |
|
Day – 1 |
300 |
400 |
700 |
|
Day -2 |
600 |
250 |
850 |
|
Day -3 |
600 |
350 |
950 |
Total of 3200 passengers travelled on the boat, with the ratio of male to female passengers being 5:3.
So, Number of male passengers travelled is 3200 × 5 / 8 = 2000
Number of female passengers travelled is 3200 – 2000 = 1200
On Day 1, 35% of all male passengers and 50% of all female passengers were on board.
Male passenger on day 1 is 2000 × 35 /100 = 700
Female passenger on day 1 is 1200 × 50 /100 = 600
On Day 2, The proportion of passengers on this day included 40% of all male passengers and 25% of all female passengers.
Male passenger on day 2 is 2000 × 40 /100 = 800
Female passenger on day 2 is 1200 × 25 /100 = 300
Male passenger on day 3 is 2000 – 700 – 800 = 500
Female passenger on day 3 is 1200 – 600 -300=300
|
|
Male Passenger |
Female passenger |
Total passenger |
|
Day – 1 |
700 |
600 |
1300 |
|
Day -2 |
800 |
300 |
1100 |
|
Day -3 |
500 |
300 |
800 |
Some male passengers travelled on multiple days, 24 male passengers travelled on both Day 1 and Day 2 (excluding Day 3).20 male and passengers travelled on both Day 2 and Day 3 (excluding Day 1).16 male passengers travelled on both Day 3 and Day 1 (excluding Day 2). 13 male passengers travelled on all three days.
Total male passenger travelled is = 2000
Male passenger travelled Only Day 1 is
= 700−(24 + 16 + 13) = 647
Male passenger travelled Only Day 2 is
= 800−(24 + 20 + 13) = 743
Male passenger travelled Only Day 3 is
=500−(16 + 20 + 13) = 451
Some female passengers travelled on multiple days, 34 female passengers travelled on both Day 1 and Day 2 (excluding Day 3).22 female passengers travelled on both Day 2 and Day 3 (excluding Day 1).40 female passengers travelled on both Day 3 and Day 1 (excluding Day 2). 9 female passengers travelled on all three days.
Total female passenger travelled = 1200
Female passenger travelled Only Day 1
= 600 − (34 + 40 + 9) = 517
Female passenger travelled Only Day 2
= 300 − (34 + 22 + 9) = 235
Female passenger travelled Only Day 3
= 300 − (40 + 22 + 9) = 229
Calculation:
Total male passengers on day 2 is [800 + 500] = 1300
Total female passengers on day 3 is [ 300 + 300] = 600
So, required ratio = 1300 : 600 = 13 : 6