Model 1 Basic Time & Distance using formula Section-Wise Topic Notes With Detailed Explanation And Example Questions
MOST IMPORTANT quantitative aptitude - 5 EXERCISES
The following question based on time & distance topic of quantitative aptitude
(a) 66 km
(b) 60 km
(c) 54 km
(d) 48 km
The correct answers to the above question in:
Answer: (b)
Let the distance between A and B be x km, then
$x/9 - x/10 = 36/60 = 3/5$
$x/90 = 3/5$
$x = 3/5 × 90$ = 54 km.
Using Rule 9,
Here, $S_1 = 9, t_1 = x, S_2 = 10, t_2 = x - 36/60$
$S_1t_ 1 = S_2t_ 2$
$9 × x = 10(x - 36/60)$
9x = 10x - 6 = 6
Distance travelled = 9 × 6 = 54 km
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Read more basic problems formulas Based Quantitative Aptitude Questions and Answers
Question : 1
A man rides at the rate of 18 km/ hr, but stops for 6 mins. to change horses at the end of every 7th km. The time that he will take to cover a distance of 90 km is
a) 6 hrs. 24 min.
b) 6 hrs. 18 min.
c) 6 hrs. 12 min.
d) 6 hrs.
Answer »Answer: (b)
90 km = 12 × 7km + 6 km.
To cover 7 km total time taken = $7/18$ hours + 6 min. = $88/3$ min.
So, (12 × 7 km) would be covered in $(12 × 88/3)$ min.
and remaining 6km is $6/18$ hrs or 20 min.
Total time = $1056/3$ + 20
= $1116/{3 × 60}$ hours = 6$1/5$ hours
= 6 hours 12 minutes.
Question : 2
A man travelled a certain distance by train at the rate of 25 kmph. and walked back at the rate of 4 kmph. If the whole journey took 5 hours 48 minutes, the distance was
a) 15 km
b) 20 km
c) 30 km
d) 25 km
Answer »Answer: (c)
Let the distance be x km.
Total time = 5 hours 48 minutes
= $5 + 48/60 = (5 + 4/5)$ hours
= $29/5$ hours
$x/25 + x/4 = 29/5$
${4x + 25x}/100 = 29/5$
5 × 29x = 29 × 100
$x = {29 × 100}/{5 × 29}$ = 20 km.
Using Rule 5,If a bus travels from A to B with the speed x km/h and returns from B to A with the speed y km/h,then the average speed will be $({2xy}/{x + y})$
Here, x = 25, y = 4
Average speed = ${2xy}/{x + y}$
= ${2 × 25 × 4}/{25 + 4} = 200/29$
Total Distance = $200/29 × 5{4}/5$
= $200/29 × 29/5$ = 40 km
Required distance = 20 km
Question : 3
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) 44 km
b) 36 km
c) 48 km
d) 32 km
Answer »Answer: (d)
Journey on foot=x km
Journey on cycle = (80 –x)km
$x/8 + {80 - x}/16 = 7$
${2x + 80 - x}/16 = 7$
x + 80 = 16 × 7 = 112
x= 112 - 80 = 32 km.
Using Rule 13,Let a man take 't' hours to travel 'x' km. If he travels some distance on foot with the speed u km/h and remaining distance by cycle with the speed v km/h,then time taken to travel on foot.Time = ${(vt - x)}/{(v - u)}$Distance travelled on foot = Time × u
Here, x = 80, t = 7, u = 8, v = 16
Time = $({vt - x}/{v - u})$
=$({16 × 7 - 80}/{16 - 8})$
=$({112 - 80}/8) = 32/8$ = 4 hrs
Distance travelled
= 4 × 8 = 32 kms
Question : 4
A train is travelling at the rate of 45km/hr. How many seconds it will take to cover a distance of $4/5$ km ?
a) 120 sec.
b) 90 sec.
c) 64 sec.
d) 36 sec.
Answer »Answer: (b)
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
Time taken = $\text"Distance"/ \text"time"$
= ${4/5}/45$ hour
= ${4 × 60 × 60}/{5 × 45}$ sec. = 64 seconds
Question : 5
A person started his journey in the morning. At 11 a.m. he covered $3/8$ of the journey and on the same day at 4.30 p.m. he covered $5/6$ of the journey. He started his journey at
a) 6.30 a.m.
b) 7.00 a.m.
c) 3.30 a.m.
d) 6.00 a.m.
Answer »Answer: (a)
Difference of time
= 4.30 p.m - 11.a.m.
= $5{1}/2$ hours $11/2$ hours
Distance covered in $11/2$ hrs
= $5/6 - 3/8 = {20 - 9}/24 = 11/24$ part
Since, $11/24$ part of the journey is covered in $11/2$ hours
$3/8$ part of the journey is covered in
= $11/2 × 24/11 × 3/8$
= $9/2$ hours = 4$1/2$ hours.
Clearly the person started at 6.30 a.m.
Question : 6
A man covers $2/15$ of the total journey by train, $9/20$ by bus and the remaining 10 km on foot. His total journey (in km) is
a) 12.8
b) 16.4
c) 24
d) 15.6
Answer »Answer: (b)
Let the total journey be of x km, then
${2x}/15 + {9x}/20 + 10 = x$
$x - {2x}/15 - {9x}/20$ = 10
${60x - 8x - 27x}/60$ = 10
${25x}/60$ = 10
$x = {60 × 10}/25$ = 24 km
GET time & distance PRACTICE TEST EXERCISES
Model 1 Basic Time & Distance using formula
Model 2 Vehicles in x/y of its usual speed
Model 3 Problems on average speed
Model 4 Time & Distance with Ratios
Model 5 Problems with Races
time & distance Shortcuts and Techniques with Examples
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Model 1 Basic Time & Distance using formula
Defination & Shortcuts … -
Model 2 Vehicles in x/y of its usual speed
Defination & Shortcuts … -
Model 3 Problems on average speed
Defination & Shortcuts … -
Model 4 Time & Distance with Ratios
Defination & Shortcuts … -
Model 5 Problems with Races
Defination & Shortcuts …
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