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1.	1). 3.75 kmph2). 0.6 kmph3). 5 kmph4). 1.5 kmph
Answer» Distance from the shore(d) = 45 km Water enter per hour in ship by hole = 4¼ tonnes in 15 min = 4.25/0.25 = 17 tonnes (? 1 HR = 60 min) Water leaving the ship per hour by pump = 12 tonnes/hr Amount of water REMAINING at the end of the hour = 17 - 12 = 5 tonnes/hr Time TAKEN to sink the ship = 60/5 = 12 hr Average speed of sailing to reach the shore just before = Distance/Time = 45/12 = 3.75 km/hr ∴ The average speed of sailing to reach the shore just before sink = 3.75 km/hr

1). 3.75 kmph2). 0.6 kmph3). 5 kmph4). 1.5 kmph

Answer»

Distance from the shore(d) = 45 km

Water enter per hour in ship by hole = 4¼ tonnes in 15 min = 4.25/0.25 = 17 tonnes

(? 1 HR = 60 min)

Water leaving the ship per hour by pump = 12 tonnes/hr

Amount of water REMAINING at the end of the hour = 17 - 12 = 5 tonnes/hr

Time TAKEN to sink the ship = 60/5 = 12 hr

Average speed of sailing to reach the shore just before = Distance/Time = 45/12 = 3.75 km/hr

∴ The average speed of sailing to reach the shore just before sink = 3.75 km/hr

Discussion

2.	Two trains start from P and Q and head towards Q and P respectively. Train from P starts at 11 pm and reaches Q at 5 pm next day. Train from Q starts at 10 pm the same day on which the train starts from station P and reaches P at 6 am the next day. At what time (approximate) will they cross each other1). 4 am2). 3 ∶ 55 am3). 2 ∶ 51 am4). 4 ∶ 05 am
Answer» Train from P starts at 11 pm and reaches Q at 5 pm next day Time taken by train P = (5 pm next day) – 11 pm = 18 hr Train from Q starts at 10 pm the same day on which the train starts from stationP and reaches P at 6 am the next day Time taken by train Q = (6 am next day) – 10 pm = 8 hr Let the distance between the station is X km Speed of first train = Distance/Time taken to reach = X/18 km/hr Speed of Second train = Distance/time taken to reach = X/8 km/hr By the time the train from P starts, train from Q ALREADY TRAVELLED for (11pm – 10 pm) = 1hr In 1 hour the train had travelled = X/8 km Now the distance between the trains = X - (X/8) = 7X/8 km As the trains are MOVING in opposite direction, hence relative speed between the trains ⇒ (X/18) + (X/8) = (4X + 9X)/ 72 = 13X/72 To cover the 7X/8 km distance, it will take = $(\frac{{\frac{{7X}}{8}}}{{\frac{{13X}}{{72}}}})$ = 63/13 =4hours 11/13 × 60 min≈ 4 hours 51 minutes So the trains will meet at (11 pm + 4 hours 51 min) ≈ 3 : 51 am

Two trains start from P and Q and head towards Q and P respectively. Train from P starts at 11 pm and reaches Q at 5 pm next day. Train from Q starts at 10 pm the same day on which the train starts from station P and reaches P at 6 am the next day. At what time (approximate) will they cross each other1). 4 am2). 3 ∶ 55 am3). 2 ∶ 51 am4). 4 ∶ 05 am

Answer»

Train from P starts at 11 pm and reaches Q at 5 pm next day

Time taken by train P = (5 pm next day) – 11 pm = 18 hr

Train from Q starts at 10 pm the same day on which the train starts from stationP and reaches P at 6 am the next day

Time taken by train Q = (6 am next day) – 10 pm = 8 hr

Let the distance between the station is X km

Speed of first train = Distance/Time taken to reach = X/18 km/hr

Speed of Second train = Distance/time taken to reach = X/8 km/hr

By the time the train from P starts, train from Q ALREADY TRAVELLED for (11pm – 10 pm) = 1hr

In 1 hour the train had travelled = X/8 km Now the distance between the trains = X - (X/8) = 7X/8 km

As the trains are MOVING in opposite direction, hence relative speed between the trains

⇒ (X/18) + (X/8) = (4X + 9X)/ 72 = 13X/72

To cover the 7X/8 km distance, it will take = $(\frac{{\frac{{7X}}{8}}}{{\frac{{13X}}{{72}}}})$ = 63/13 =4hours 11/13 × 60 min≈ 4 hours 51 minutes

So the trains will meet at (11 pm + 4 hours 51 min) ≈ 3 : 51 am

Discussion