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) 44 km
(b) 36 km
(c) 48 km
(d) 32 km
The correct answers to the above question in:
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
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Read more basic problems formulas Based Quantitative Aptitude Questions and Answers
Question : 1
A bullock cart has to cover a distance of 120 km. in 15 hours. If it covers half of the journey in $3/5$th time, the speed to cover the remaining distance in the time left has to be
a) 15 km/hr
b) 10 km/hr
c) 6.67 km/hr
d) 6.4 km/hr
Answer »Answer: (c)
Using Rule 1,
Remaining time
= $2/5 × 15 = 6$ hours
Required speed
= $60/6$ = 10 kmph
Question : 2
A man walks 'a' km in 'b' hours. The time taken to walk 200 metres is
a) ${ab}/200$ hours
b) $b/a$ hours
c) $b/{5a}$ hours
d) ${200b}/a$ hours
Answer »Answer: (b)
Using Rule 1,
Man's speed = $\text"Distance"/ \text"Time"$
= $a/b$ kmph = ${1000a}/b$ m/hour
Time taken in walking 200 metre
= $200/{{1000a}/b} =b/{5a}$ hours
Question : 3
A man crosses a road 250 metres wide in 75 seconds. His speed in km/hr is :
a) 15
b) 12.5
c) 12
d) 10
Answer »Answer: (b)
Using Rule 1,
Speed = $\text"Distance"/\text"Time" = 250/75$
= $10/3$ m/sec = $10/3 × 18/5$ km/hr
[Since, 1 m/s = $18/5$ km/hr]
= 2 × 6 km/hr. = 12 km/hr.
Question : 4
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 : 5
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 : 6
A and B travel the same distance at speed of 9 km/hr and 10 km/ hr respectively. If A takes 36 minutes more than B, the distance travelled by each is
a) 66 km
b) 60 km
c) 54 km
d) 48 km
Answer »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
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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