The following table shows the distance travelled by a boat moving upstream (in…
2023
The following table shows the distance travelled by a boat moving upstream (in km) during five different days of a week from Monday to Friday, along with the speed of boat (in km/hour), speed of stream (in km/hour) and total time taken (in hours). Some data is missing in the table (indicated as '—') that you are expected to calculate, if required. Based on the data in the table, answer the questions that follow.
Day-wise distance travelled by the boat and other details
Days | Distance Upstream (km) | Speed of Boat (km/hour) | Speed of Stream (km/hour) | Total Time Taken (hours) |
|---|---|---|---|---|
Monday | 320 | — | 4 | — |
Tuesday | — | — | — | 75 |
Wednesday | 270 | — | 6 | — |
Thursday | — | 11 | 7 | — |
Friday | 324 | — | — | 72 |
Note: (1) Distance Upstream = Distance Downstream, if not stated otherwise.
Note: (2) Total Time Taken = Downstream Time + Upstream Time
On Thursday, the difference between the time taken by the boat to cover 'X' km upstream and (X + 120) km downstream is 26 hours. Had the boat covered the same distance upstream as downstream, then what would have been the difference in the time taken?
Answer: D. 56 hours — CONCEPT For a boat whose speed in still water is b and stream speed is s, upstream speed is b − s and downstream speed is b + s. Time equals distance divided…
- A.
58 hours
- B.
62 hours
- C.
48 hours
- D.
56 hours
Show answer & explanation
Correct answer: D
CONCEPT
For a boat whose speed in still water is b and stream speed is s, upstream speed is b − s and downstream speed is b + s. Time equals distance divided by speed, so the difference in travel times is found by subtracting the two time expressions.
APPLICATION
The Thursday upstream and downstream speeds are 11 − 7 = 4 km/h and 11 + 7 = 18 km/h.
Let the original upstream distance be X km; the downstream distance is X + 120 km. Since the upstream journey takes longer, X/4 − (X + 120)/18 = 26.
Multiplying by 36 gives 9X − 2(X + 120) = 936, so 7X = 1176 and X = 168 km.
The stated downstream distance is X + 120 = 288 km. For equal upstream and downstream distances, use 288 km for each journey.
The upstream time is 288/4 = 72 hours and the downstream time is 288/18 = 16 hours. Their difference is 72 − 16 = 56 hours.
CROSS-CHECK
For the original unequal distances, 168/4 = 42 hours and 288/18 = 16 hours; 42 − 16 = 26 hours, matching the given condition.
RESULT
The required difference in time is 56 hours.