Answer: Option D
Explanation:
speed of hour needle = 0.5°/min
= \(\frac {0.5} {60}\) =(\(\frac {1} {120}\))°/sec
speed of seconds needle = 360°/min
=(\(\frac {360} {60}\))°/sec
i.e, =(\(\frac {speed of seconds needle} {speed of hours needle}\))
=(\(\frac {6} {\frac {1}{120}}\)) = 720 : 1
2. A man drives a car and reaches his destination in 4 hours. Had he increased hi s speed by 10 km/hr, he would have reached in 3 hours, 12 minutes. What distance did the man cover?
Answer: Option C
Explanation:
Let distance be D km
Let initial speed be 5 km/hr
According to the question
\(\frac {D} {S}\) = 4 ……(1)
\(\frac {D} {S + 10}\) = 3 \(\frac {1} {5}\) …..(2)
Divide (1) by (2)
\(\frac {S + 10} {S}\) = \(\frac {5} {4}\)
S = 40 km/hr
i.e, D = 40 × 4 = 160 km
3. The speed of a boat in downstream direction is 14 km/hour and in upstream direction is 8 km/hour. Find the speed of this boat in still water :
Answer: Option D
Explanation:
Let the speed of boat in still water be x km/hr
Let the speed of stream be y km/hr
According to the question,
x + y = 14
x – y = 18
2x = 22
x = 11 km/hr
4. Manoj can complete a journey in 10 hours. He travels first half of the journey at the speed of
21 kmph and second half of the journey at the speed of 24 kmph. Find the total journey :
Answer: Option D
Explanation:
Average speed = \(\frac {21 * 24} {21 + 24}\)
Total Distance = 22.4 * 10 = 224 km
5. A train, 270 metres long, is running at the speed of 120 kmph. I t crosses another train, which is running at the speed of 80 kmph in opposite direction on parallel track, in 9 seconds. What is the length of another train?
Answer: Option A
Explanation:
Relative speed = (120 + 80) * \(\frac {5} {18}\) m/s
= 200 * \(\frac {5} {18}\)
Let the length of other train be x m.
According to question, \(\frac {270 + x} {200 \frac{5}{18}}\) = 9
x = 230 m
Answer: Option C
Explanation:
Q =/30h – \(\frac {11} {2}\) m/ = /30 * 3 – \(\frac {11} {2}\) * 40/ = 130°
7. Two trains approach each other at 30 km/hr and 27 km/hr from two places 342 km apart. After how many hours will they meet ?
Answer: Option B
Explanation:
Time after the trains meet = \(\frac {342 km} {(30 + 27) km/hr}\) = 6 hours
8. The speed of a 150 m long train is 50 kmph. How much time will it take to pass a 600 m long platform ?
Answer – Option B
Explanation:
50km / hr ? (\(50 \frac {5} {18}\)) m/s
= \(\frac {25 * 5} {9}\) m/s
\(\frac {125} {9}\) m/s
Time taken = \(\frac {(150 + 600)m} {(\frac {125}{9}) m/s}\)
= 54 seconds
9. A person travels a certain distance on a bicycle with a certain speed. Had he moved 3 km/hour faster, he would have taken 40 minutes less. Had he moved 2 km/hour slower, he would have taken 40 minutes more. Slower speed of the person, in km/hour, is
Answer: Option B
Explanation:
3 km / hr faster … \(\frac {2} {3}\) hr less
2 km / hr slower … \(\frac {2} {3}\) hr more
Let initial speed = V
v = \(\frac {{v}_{1} {v}_{2} (t ÷ t)} {{v}_{1} {t}_{2} – {v}_{2} {t}_{1}}\)
\(\frac {2 {v}_{1} {v}_{2}} {{v}_{1} – {v}_{2}}\)(i.e, \({t}_{1}{t}_{2} \) = 40min)
\(\frac {2 * 3 * 2} {3 – 2}\) = 2
i.e, slower speed =(12 – 2) km/hr = 10 km/hr
10. A and B can walk around a circular path in 4 minutes and 9 minutes respectively. If they start
from the same point in the same direction, after how much time will they meet again for first time?
Answer: Option C
Explanation:
Let length of track = LCM (4 and 9) = 36 m
speed of A = \(\frac {36} {4}\) = 9 m/min
speed of B = \(\frac {36} {9}\) = 4 m/min
i.e, Time = \(\frac {36 m} {(9 – 4) m/min}\) = 7 min 12 sec
Answer: Option A
Explanation:
\({T}_{1} : {T}_{2} \) = 4 : 3.5
\({V}_{1} : {V}_{2} \) = 3.5 : 4
Let total distance = 4 × 3.5x
Distance covered by train 1 till 6 : 30 am = 1.5 × 3.5x
i.e, Meeting time\(\frac {Distance left}{Relative speed} \) = \(\frac {14x – 5.25x}{75x} \)
= 1.16 hours
i.e 7 : 40 am
12. A person can row 9 km/hour in still water and he finds that it takes him twice as much time to row upstream as to row downstream the same distance. The speed of the current, in km/hour, is
Answer: Option B
Explanation:
speed in still water = 9 km/ pr
Time up : Time Down = 2 : 1
i.e,speed up : speed Down = 1 : 2
speed in still water = \(\frac {1}{2}\)(x ÷ 2x) = 9
x = 6 km/ pr
speed of current = \(\frac {1}{2}\)(2x – x) = 3
13. Anu travel by car and covers \(\frac{1}{4}\)th of her journey with a speed of 60 km/hour, 40% her journey with a speed of 50 km/hour, and the rest with a speed of 42 km/hours. The average speed (km/hour) for the whole journey is about
Answer: Option B
Explanation:
Distance = \( x\frac {1 } {4} + x\frac {2} {5} + x\frac {35} {100}\)
Time = \( \frac {x} {4 * 60} + \frac {2x} {5 * 50} + \frac {35x} {100 * 42}\)
i.e, Avg speed = \( \frac {Total Distance} {Total Time}\) = 48.8km / pr
14. Two places A and B are 220 km apart on a highway Hari starts from A and Juhi from B at the same time on the same day using cars. If they travel in the same direction (A to B ), hey meet in 5 \(\frac {1} {2}\) hour s, but in 2 hour s 45 mi nut es when travelling towards each other. Speed of the car of Juhi, in km/hour, is
Answer: Option A
Explanation:
Let speed of A be x km/hr
let speed of B be y km/hr
\(\frac {220} {x – y}\) = \( 5 \frac {1} {2}\) = \(\frac {11} {2}\)
\(\frac {220} {x + y}\) = \( 2 \frac {3} {4}\) = \(\frac {11} {4}\)
x = 60 km/hr
y = 20 km/hr
= 20 km/hr
15. A covers a certain distance in a certain time, if B covers half of this distance in the double time, the ratio of speeds of A and B is
Answer: Option B
Explanation:
According to question, \(\frac {D} {{S}_{A}}\)
\(\frac {\frac {D}{2}} {{S}_{B}}\)
\( {S}_{A} : {S}_{B}\) = 4 : 1
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