Model 6 Change in speed Vs Change with time travel Section-Wise Topic Notes With Detailed Explanation And Example Questions
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The following question based on trains topic of quantitative aptitude
(a) 7 km
(b) 12 km
(c) 16 km
(d) 6 km
The correct answers to the above question in:
Answer: (b)
Let the distance be x km.
$x/10 - x/12 = 12/60$
${6x - 5x}/60 = 1/5$
$x = 1/5 × 60$ = 12 km.
Using Rule 10,
Here, $S_1 = 10, t_1 = 6, S_2 = 12, t_2$ = 6
Distance = ${(S_1 × S_2)(t_1 + t_2)}/{S_2 - S_1}$
= ${(10 × 12)(6 + 6)}/{12 - 10}$
= ${120 × 12}/2$
= 60 × $12/60$ km = 12km
Discuss Form
Read more changing speed with time travel Based Quantitative Aptitude Questions and Answers
Question : 1
If a boy walks from his house to school at the rate of 4 km per hour, he reaches the school 10 minutes earlier than the scheduled time. However, if he walks at the rate of 3 km per hour, he reaches 10 minutes late. Find the distance of his school from his house.
a) 4 km
b) 6 km
c) 4.5 km
d) 5 km
Answer »Answer: (a)
Let the distance of school be x km, then
$x/3 - x/4 = 20/60$
$x/12 = 1/3 ⇒ x =12/3 = 4$ km
Using Rule 10,
Here, $S_1 = 3, t_1 = 10, S_2 = 4, t_2$ = 10
Distance = ${(S_1 × S_2)(t_1 + t_2)}/{S_2 - S_1}$
= ${(3 × 4)(10 + 10)}/{4 - 3}$
= $12 × 20/60$ = 4 km
Question : 2
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) 35
b) 36$2/3$
c) 40
d) 20
Answer »Answer: (c)
Let the distance be x km and initial speed be y kmph.
According to question,
$x/y - x/{y + 3} = 40/60$ ...(i)
and, $x/{y - 2} - x/y = 40/60$ ...(ii)
From equations (i) and (ii),
$x/y - x/{y + 3} = x/{y - 2} - x/y$
$1/y - 1/{y + 3} = 1/{y - 2} - 1/y$
${y + 3 -y}/{y(y + 3)} = {y - y + 2}/{y(y - 2)}$
3 (y - 2) = 2 (y + 3)
3y - 6 = 2y + 6
y = 12
From equation (i),
$x/12 - x/15 =40/60$
= ${5x - 4x}/60 = 2/3$
$x = 2/3 × 60$ = 40
Distance = 40 km.
Question : 3
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) 13 minutes 20 sec
b) 13 minutes
c) 11 minutes 20 sec
d) 10 minutes
Answer »Answer: (a)
Using Rule 1,
Speed of train = $\text"Distance"/\text"Time"$
= $10/{12/60}$ kmph
= ${10 × 60}/12 = 50$ kmph
New speed = 45 kmph
∴ Required time = $10/45$ hour
= $2/9 × 60$ minutes
= $40/3$ minutes or 13 minutes 20 seconds
Question : 4
If a train runs at 40 km/hour, it reaches its destination late by 11 minutes. But if it runs at 50 km/ hour, it is late by 5 minutes only. The correct time (in minutes) for the train to complete the journey is
a) 15
b) 19
c) 21
d) 13
Answer »Answer: (b)
If the distance be x km,
then $x/40 - x/50 = 6/60$
$x/4 - x/5 = 1$
x = 20 km.
Required time
= $(20/40)$ hour - 11 minutes
= $(1/2 × 60 - 11)$ minutes
= 19 minutes
Question : 5
A car can cover a certain distance in 4$1/2$ hours. If the speed is increased by 5 km/hour, it would take $1/2$ hour less to cover the same distance. Find the slower speed of the car.
a) 40 km/hour
b) 45 km/hour
c) 60 km/hour
d) 50 km/hour
Answer »Answer: (a)
Let the initial speed of the car be x kmph and the distance be y km.
Then, y = $9/2$ x ...(i)
and, y = 4 (x + 5) ...(ii)
${9x}/2 = 4(x + 5)$
9x = 8x + 40
x = 40 kmph
trains Shortcuts and Techniques with Examples
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Model 1 Train Vs Train in same direction
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Model 2 Train Vs Train in opposite direction
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Model 3 Train Vs Bridge/Platform
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Model 4 Train Vs Pole/Signal Post/Man
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Model 5 Train Vs Both platform and a man/a pole
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Model 6 Change in speed Vs Change with time travel
Defination & Shortcuts …
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