Common Information
A low-cost airline company connects ten Indian cities, A to J. The table below gives the distance between a pair of airports and the corresponding price charged by the company.
Travel is permitted only from a departure airport to an arrival airport. The customers do not travel by a route where they have to stop at more than two intermediate airports.
Table below can be scrolled horizontally
Sector No. |
Airport of |
Airport of |
Distance between |
Price (Rs.) |
1 |
A |
B |
560 |
670 |
2 |
A |
C |
790 |
1350 |
3 |
A |
D |
850 |
1250 |
4 |
A |
E |
1245 |
1600 |
5 |
A |
F |
1345 |
1700 |
6 |
A |
G |
1350 |
2450 |
7 |
A |
H |
1950 |
1850 |
8 |
B |
C |
1650 |
2000 |
9 |
B |
H |
1750 |
1900 |
10 |
B |
I |
2100 |
2450 |
11 |
B |
J |
2300 |
2275 |
12 |
C |
D |
460 |
450 |
13 |
C |
F |
410 |
430 |
14 |
C |
G |
910 |
1100 |
15 |
D |
E |
540 |
590 |
16 |
D |
F |
625 |
700 |
17 |
D |
G |
640 |
750 |
18 |
D |
H |
950 |
1250 |
19 |
D |
J |
1650 |
2450 |
20 |
E |
F |
1250 |
1700 |
21 |
E |
G |
970 |
1150 |
22 |
E |
H |
850 |
875 |
23 |
F |
G |
900 |
1050 |
24 |
F |
I |
875 |
950 |
25 |
F |
J |
970 |
1150 |
26 |
G |
I |
510 |
550 |
27 |
G |
J |
830 |
890 |
28 |
H |
I |
790 |
970 |
29 |
H |
J |
400 |
425 |
30 |
I |
J |
460 |
540 |
Q. |
Common Information Question: 1/5 What is the lowest price, in rupees, a passenger has to pay for travelling by the shortest route from A to J? |
✖ A. | 2275 |
✖ B. | 2850 |
✖ C. | 2890 |
✔ D. | 2930 |
✖ E. | 3340 |
Solution:
Option(D) is correct
Possible routes from A to J are as shown in the table below.
Table below can be scrolled horizontally
Route |
Distance |
Price |
ABJ |
2860 |
2945 |
ADJ |
2500 |
3700 |
AFJ |
2315 |
2850 |
AGJ |
2180 |
3340 |
AHJ |
2350 |
2275 |
ABHJ |
2710 |
2995 |
ABIJ |
3120 |
3660 |
ACDJ |
2900 |
4250 |
ACFJ |
2170 |
2930 |
ACGJ |
2530 |
3340 |
ADFJ |
2445 |
3100 |
ADGJ |
2320 |
2890 |
ADHJ |
2200 |
2925 |
AEFJ |
3465 |
4450 |
AEGJ |
3045 |
3640 |
AEHJ |
2495 |
2900 |
AFGJ |
3075 |
3640 |
AFIJ |
2680 |
3190 |
AGIJ |
2320 |
3540 |
AHIJ |
3200 |
3360 |
The shortest distance is by the route ACFJ.
The price is:
$=1350 + 430 + 1150$
$=\textbf{Rs. 2930}$
Hence, option D.