Directions: Read the table carefully and answer the following question. The…
2023
Directions: Read the table carefully and answer the following question.
The table shows the data about distance (km) covered from one point to another point by the vehicle used between each point and speed of each vehicle (km/hr). i.e., If one person wants to travel from P to S, then he/she can only use vehicle available at the point P
Note: ** means there is no direct connection between given points
Find the minimum possible sum of the time (in hours) taken to cover distance from P to S and from R to S.
- A.
17⅔
- B.
18⅔
- C.
16
- D.
25
- E.
12
Attempted by 1 students.
Show answer & explanation
Correct answer: A
Concept
Time = Distance ÷ Speed. For a multi-leg journey, the total time is the sum of the time on each leg, and on every leg the speed is fixed by the vehicle available at the starting point of that leg (Taxi=80 at P, Bus=50 at Q, Car=60 at R, Bike=25 at S). To minimise a journey's time, list every legal route, add the per-leg times, and keep the smallest. "**" marks a missing direct link, so such a leg cannot be used.
Application
Leg 1 — P to S (minimise):
Direct P→S: distance 520 km at the P-vehicle speed 80 km/hr → 520 ÷ 80 = 13/2 = 6.5 hr.
Via Q (P→Q→S): 240 ÷ 80 + 400 ÷ 50 = 3 + 8 = 11 hr.
P→R is "**" (no link), so no route through R. Minimum P→S = 13/2 hr (6.5 hr).
Leg 2 — R to S (minimise):
Direct R→S is "**", so it must be reached through another point.
Via P (R→P→S): 280 ÷ 60 + 520 ÷ 80 = 14/3 + 13/2 = (28 + 39)/6 = 67/6 ≈ 11.17 hr.
Via Q (R→Q→S): 480 ÷ 60 + 400 ÷ 50 = 8 + 8 = 16 hr.
67/6 hr < 16 hr, so minimum R→S = 67/6 hr.
Required sum: 13/2 + 67/6 = (39 + 67)/6 = 106/6 = 53/3 = 17⅔ hr.
Cross-check
Decimal check: 6.5 + 11.1667 = 17.6667 hr, and 53/3 = 17.6667 hr — consistent. The slower alternatives (using the 16 hr R→S route, or the 11 hr P→S route) only increase the sum, confirming 53/3 hr is the minimum.