time and distance multiple choice questions
Two men start together to walk a certain distance, one at 4 km/h and another at 3 km/h. The former arrives half an hour before the latter. Find the distance.
(a) 8 km
(b) 7 km
(c) 6 km
(d) 9 km
(e) 5 km
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Answer: (c)
If the required distance be x km, then
\(\displaystyle \frac{x}{3}-\frac{x}{4}=\frac{1}{2}\)
\(\displaystyle \frac{{4x-3x}}{{12}}=\frac{1}{2}\)
\(\displaystyle \frac{x}{{12}}=\frac{1}{2}\Rightarrow x=6km\)
A train covers a distance of 10 km in 12 minutes. If its speed is decreased by 5 km/hr, the time taken by it to cover the same distance will be :
(a) 10 minutes
(b) 13 minutes 20 sec
(c) 13 minutes
(d) 11 minutes 20 sec
(e) 12 minutes
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Answer: (b)
Speed of train = \(\displaystyle \frac{{dis\tan ce}}{{time}}\)
\(\displaystyle \frac{{10}}{{\frac{{12}}{{60}}}}kmph=\frac{{10\times 60}}{{12}}=50kmph\)
New speed = 45 kmph
Required time = \(\displaystyle \frac{{10}}{{45}}hour\)
\(\displaystyle \frac{2}{9}\times 60\min utes\)
\(\displaystyle \frac{{40}}{3}\min utes\)
= 13 minutes 20 seconds
A man walks ‘a ’ km in ‘b ’ hours. The time taken to walk 200 metres is
(a) \(\displaystyle \frac{{200b}}{a}hours\)
(b) \(\displaystyle \frac{b}{{5a}}hours\)
(c) \(\displaystyle \frac{b}{{a}}hours\)
(d) \(\displaystyle \frac{{ab}}{{200}}hours\)
(e) \(\displaystyle \frac{{200}}{{ab}}hours\)
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Answer: (b)
Man’s speed = \(\displaystyle \frac{{dis\tan ce}}{{time}}\)
\(\displaystyle \frac{a}{b}kmph\)
\(\displaystyle \frac{{1000a}}{b}m/hour\)
Time taken in walking 200 metre = \(\displaystyle \frac{{200}}{{\frac{{1000a}}{b}}}=\frac{b}{{5a}}hours\)
You arrive at your school 5 minutes late if you walk with a speed of 4 km/h, but you arrive 10 minutes before the scheduled time if you walk with a speed of 5 km/h. The distance of your school from your house (in km) is
(a) 4
(b) 5
(c) 10
(d) 2
(e) 8
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Answer: (b)
If the required distance be = x km, then
\(\displaystyle \frac{x}{4}-\frac{x}{5}=\frac{{10+5}}{{60}}\)
\(\displaystyle \frac{{5x-4x}}{{20}}=\frac{1}{4}\)
\(\displaystyle \frac{x}{{20}}=\frac{1}{4}\)
\(\displaystyle x=\frac{1}{4}\times 20=5km\)
A man travelled a distance of 80 km in 7 hrs partly on foot at the rate of 8 km per hour and partly on bicycle at 16km per hour. The distance travelled on the foot is
(a) 32 km
(b) 48 km
(c) 36 km
(d) 44 km
(e) 49 km
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Answer: (a)
Journey on foot = x km
Journey on cycle = (80 – x ) km
\(\displaystyle \frac{x}{8}+\frac{{80-x}}{{16}}=7\)
\(\displaystyle \frac{{2x+80-x}}{{16}}=7\)
x + 80 = \(\displaystyle 16\times 7=112\)
x = 112 – 80 = 32 km.
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