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Arithmetic: Time Speed Distance Test-5

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Question 1
If a man walks 20 km at 5 km/hr, he will be late by 40 minutes. If he walks at 8 km per hr, how early from the fixed time will he reach?
A
15 minutes
B
25 minutes
C
50 minutes
D
$ \displaystyle 1\frac{1}{2}$Minutes
Question 1 Explanation: 
The time taken by the man is 20 /5 = 4 hours.
If he is 40 mins late he should have reached by 3 hours 20 mins. = 200 mins
When he travels at 8 Km/hr, the person would reach at 20/8 = 2 hours 30 mins. = 150 mins
He has reached 200-150 = 50 mins earlier.
Question 2
If a man reduces his speed to 2/3, he takes 1 hour more in walking a certain distance. The time (in hours) to cover the distance with his normal speed is:
A
2
B
1
C
3
D
1.5
Question 2 Explanation: 
According to the question A reduction of speed to 2/3 or original means the time taken will be in the ratio of  2: (3-2)= 2:1 . The time taken will be double. Therefore, now he will take 2 hours to walk the same distance.
Question 3
A student rides on bicycle at 8 km/hour and reaches his school 2.5 minutes late. The next day he increases his speed to 10 km/hour and reaches school 5 minutes early. How far is the school from his house?
A
5/8 km
B
8 km
C
5 km
D
10 km
Question 3 Explanation: 
Let t be the correct time to reach the school and all the speed be considered unit-less as the multiplying factor for conversion will cancelled on both sides of equation,
(t+2.5)8=10(t-5)
8t + 20 = 10t - 50
2t = 70
t=35 mins.
Distance from school =$ 10\times \frac{35-5}{60}=5km$
Question 4
A man covered a certain distance at some speed. Had he moved 3 km per hour faster, he would have taken 40 minutes less. If he had moved 2 km per hour slower, he would have taken 40 minutes more. The distance (in km) is:
A
20
B
35
C
362/3
D
40
Question 4 Explanation: 
Let the distance be x km and initial speed be y kmph.
Acc. to the given statements
$ \displaystyle \begin{array}{l}\frac{x}{y}-\frac{x}{y+3}=\frac{40}{60}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...............\left( i \right)\\and.\\\frac{x}{y-2}-\frac{x}{y}=\frac{40}{60}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,....................\left( ii \right)\\From\,\,\,\,equations\,\,\,\left( i \right)\,\,\,\,and\,\,\,\left( ii \right).\\\frac{x}{y}-\frac{x}{y+3}=\frac{x}{y-2}-\frac{x}{y}\\\Rightarrow \frac{1}{y}-\frac{1}{y+3}=\frac{1}{y-2}-\frac{1}{y}\\\Rightarrow \frac{y+3-y}{y\,\left( y+3 \right)}=\frac{y-y+2}{y\,\left( y-2 \right)}\\\Rightarrow 3\,\left( y-2 \right)=2\left( y+3 \right)\\\Rightarrow 3y-6=2y+6\\\Rightarrow y=12\\From\,\,\,\,equation\,\,\,\left( i \right).\\\frac{x}{12}-\frac{x}{15}=\frac{40}{60}\Rightarrow \frac{5x-4x}{60}=\frac{2}{3}\\\Rightarrow x=\frac{2}{3}\times 60=40\\\therefore \,\,\,Dis\tan ce=40\,km.\end{array}$
Question 5
Starting from his house one day, a student walks at a speed of 21/2 km/h, and reaches his school 6 minutes late. Next day at the same time he increases his speed by 1 kmph. and reaches the school 6 minutes early. How far is the school from his house?
A
(a) 2 km
B
(b) 11/2 km
C
(c) 1 km
D
(d) 13/4 km
Question 5 Explanation: 
Let the speed be s kmph and t mins =appropriate time.
5/2(t+6) = (7/2) (t-6)
5t+30 = 7t -42
2t=72
t= 36 mins
s=7/2 t= 30 mins.=1/2 hour
d= 7/2 x 1/2= 13/4 km
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