Directions for question
In the internationally famed Agri-Horticulture Flower Show held in the winters of Alipore, Kolkata every year, 44 participants from West Bengal took part after the post pandemic reopening in January 2023. All of them participated in any one of the following four different categories of flowers namely Roses, Dahlias, Orchids and Lilies. Each participant was from one of the following four districts of 24-Parganas, Midnapore, Jalpaiguri and Nadia of West Bengal.
The first bar-graph shows the distribution of the participants according to the districts, with the names of the districts disguised as WB1, WB2, WB3 and WB4. The second bar-graph shows the distribution of the participants according to their category, with the names of the categories disguised as F1, F2, F3 and F4.
The following information were also known :
a) Had there been one more participant from 24-Parganas and one less participant from Jalpaiguri, the number of participants from 24-Parganas and Jalpaiguri would be equal
b) Had there been one more participant from Midnapore and one less participant from Nadia, the number of participants from Midnapore and Nadia would be equal
c) Had there been two more participants in Orchids and two less participants in Dahlias, the number of participants in Orchids and Dahlias would be equal
d) The number of participants from 24-Parganas in all the four categories was distinct natural numbers
e) The number of participants from Nadia in Orchids was 1
Question
How many participants of the Agri-Horticulture Flower Show held in Alipore, Kolkata, in the category of Orchids, participated from Jalpaiguri ?
3
-
-
-
Observing the data provided in both the first and second graphs, which is basically the same, we can conclude the following :
Graph 1 &2 |
F1 | F2 | F3 | F4 |
WB1 | 3 | 5 | 3 | 2 |
WB2 | 1 | 3 | 2 | 5 |
WB3 | 4 | 2 | 4 | 1 |
WB4 | 2 | 4 | 1 | 2 |
We can further go ahead with the totals :
Graph 1 &2 |
F1 | F2 | F3 | F4 | TOTAL |
WB1 | 3 | 5 | 3 | 2 | 13 |
WB2 | 1 | 3 | 2 | 5 | 11 |
WB3 | 4 | 2 | 4 | 1 | 11 |
WB4 | 2 | 4 | 1 | 2 | 9 |
TOTAL | 10 | 14 | 10 | 10 | 44 |
Now, from information no (d), we can conclude that WB2 could only be 24-Parganas
From information no (a), and the knowledge that WB2 is 24-Parganas, we can conclude that WB1 could only be Jalpaiguri
From information no (b) we know that Midnapore had two participants more than Nadia. So we can conclude that WB3 could only be Midnapore and WB4 could only be Nadia
From information no (c) we know that the participants in Dahlias were four more than the participants in Orchids. Hence we can conclude that F2 could only be Dahlias.
From information no (e) and the knowledge that WB4 is Nadia, we can conclude that F3 could only be Orchids
However, there is no information to let us know who among F1 and F4 were Roses and Lilies respectively
Hence, we can finally conclude :
Graph 1&2 |
F1 (Roses/Lilies) |
F2 (Dahlias) |
F3 (Orchids) |
F4 (Lilies/Rose) |
TOTAL |
WB1 (Jalpaiguri) |
3 | 5 | 3 | 2 | 13 |
WB2 (24-Parganas) |
1 | 3 | 2 | 5 | 11 |
WB3 (Midnapore) |
4 | 2 | 4 | 1 | 11 |
WB4 (Nadia) |
2 | 4 | 1 | 2 | 9 |
TOTAL | 10 | 14 | 10 | 10 | 44 |
Hence, 3 participants of the Agri-Horticulture Flower Show held in Alipore, Kolkata, in the category of Orchids, participated from Jalpaiguri