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) 8 km
(b) 3 km
(c) 2 km
(d) 5 km
The correct answers to the above question in:
Answer: (b)
Let the required distance be x km.
Then, $x/3 - x/5 = 24/60$
${5x - 3x}/15 = 2/5$
${2x}/3 = 2$ ⇒ 2x = 2 × 3
x = 3 km
Using Rule 10,
Here, $S_1 = 3, t_1 = 9, S_2 = 5, t_2$ = 15
Distance = ${(S_1 × S_2)(t_1 + t_2)}/{S_2 - S_1}$
= ${(3 × 5)(9 + 15)}/{5 - 3}$
= $15/2 × 24/60$ = 3 km
Discuss Form
Read more changing speed with time travel Based Quantitative Aptitude Questions and Answers
Question : 1
A train covers a distance between station A and station B in 45 minutes. If the speed of the train is reduced by 5 km/hr, then the same distance is covered in 48 minutes. The distance between station A and B is
a) 64 km
b) 80 km
c) 55 km
d) 60 km
Answer »Answer: (d)
Using Rule 1,Distance = Speed × TimeSpeed = $\text"Distance"/\text"Time"$ , Time = $\text"Distance"/\text"Speed"$1 m/s = $18/5$ km/h, 1 km/h = $5/18$ m/s
Let the distance between stations be x km, then speed of train
= $x/{45/60} = {4x}/3$ kmph
$x/{{4x}/3 - 5} = 48/60$
${3x}/{4x - 15} = 4/5$
16x - 60 = 15x
x = 60 km
Question : 2
If a train runs at 70 km/hour, it reaches its destination late by 12 minutes. But if it runs at 80 km/ hour, it is late by 3 minutes. The correct time to cover the journey is
a) 2 hours
b) 1 hour
c) 59 minutes
d) 58 minutes
Answer »Answer: (b)
Distance of journey = x km
Difference of time
= 12 - 3 = 9 minutes
= $9/60$ hour = $3/20$ hour
$x/70 - x/80 = 3/20$
$x/7 - x/8 = 3/2$
${8x - 7x}/56 = 3/2$
$x/56 = 3/2$
$x = 3/2 × 56$ = 84 km
∴ Required correct time
= $84/70$ hours - 12 minutes
= $(84/70 × 60 - 12)$ minutes
= 72 - 12 = 60 minutes
= 1 hour
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) 8 km
b) 5 km
c) 10 km
d) $5/8$ km
Answer »Answer: (b)
Let x km. be the required distance.
Difference in time
= 2.5 + 5 = 7.5 minutes
= $7.5/60$ hrs. = $1/8$ hrs.
Now, $x/8 - x/10 = 1/8$
= ${5x - 4x}/40 = 1/8$
$x = 40/8$ = 5 km.
Using Rule 10,If a man travels at the speed of $s_1$, he reaches his destination $t_1$ late while he reaches $t_2$ before when he travels at $s_2$ speed, then the distance between the two places is D = ${(S_1 × S_2)(t_1 + t_2)}/{S_2 - S_1}$
Here, $S_1 = 8, t_1 = 2.5, S_2 = 10, t_2 = 5$
Distance = ${(S_1 × S_2)(t_1 + t_2)}/{S_2 - S_1}$
= ${(8 × 10)(2.5 + 5)}/{10 - 8}$
= $40 × {7.5}/60$ = 5 km
Question : 4
A student goes to school at the rate of 2$1/2$ km/h and reaches 6 minutes late. If he travels at the speed of 3 km/h. he is 10 minutes early. The distance (in km) between the school and his house is
a) 4
b) 3
c) 1
d) 5
Answer »Answer: (a)
Let the required distance be x km.
$x/{5/2} - x/3 = 16/60$
${2x}/5 - x/3 = 4/15$
${6x - 5x}/15 = 4/15 ⇒ x = 4$ km.
Using Rule 10,
Here, $S_1 = 2{1}/2 , t_1 = 6, S_2 = 3, t_2$ = 10
Distance = ${(S_1 × S_2)(t_1 + t_2)}/{S_2 - S_1}$
= ${5/2 × 3(6 + 10)}/{3 - 5/2}$
= $15 × 16/60$ km = 4 km
Question : 5
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 : 6
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.
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
Defination & Shortcuts … -
Model 6 Change in speed Vs Change with time travel
Defination & Shortcuts …
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