Model 4 Time & Distance with Ratios 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) 3 : 2
(b) 3 : 4
(c) 4 : 3
(d) 2 : 3
The correct answers to the above question in:
Answer: (d)
Speed = $\text"Distance"/ \text"Time"$
∴ Speed of car : Speed of train
= $80/2 : 180/3$ = 40 : 60 = 2 : 3
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Read more problems with ratios Based Quantitative Aptitude Questions and Answers
Question : 1
It takes 8 hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the car is
a) 3 : 2
b) 3 : 4
c) 4 : 3
d) 2 : 3
Answer »Answer: (b)
Using Rule 1,
Speed of train = x kmph
Speed of car = y kmph
Case I,
$120/x + {600 - 120}/y$ = 8
$120/x + 480/y$ = 8
$15/x + 60/y$ = 1 ...(i)
Case II,
$200/x + 400/y$ = 8 hours 20 minutes
$200/x + 400/y = 8{1}/3$ hours = $25/3$
$8/x + 16/y = 1/3$
$24/x + 48/y$ = 1 ...(ii)
$15/x + 60/y = 24/x + 48/y$
$24/x - 15/x = 60/y - 48/y$
$9/x = 12/y$
$x/y = 9/12 = 3/4$ = 3 : 4
Question : 2
The speeds of three cars are in the ratio of 1 : 3 : 5. The ratio among the time taken by these cars to travel the same distance is
a) 15 : 3 : 5
b) 15 : 5 : 3
c) 5 : 3 : 1
d) 3 : 5 : 15
Answer »Answer: (d)
Speed ∝ $1/\text"Time"$
Required ratio of time
= $1 : 1/3 : 1/5$
= 15 : $1/3 × 15 : 1/5 × 15$
= 15 : 5 : 3
Question : 3
A truck covers a distance of 550 metres in 1 minute whereas a bus covers a distance of 33 kms in 45 minutes. The ratio of their speed is :
a) 3 : 5
b) 3 : 4
c) 50 : 3
d) 4 : 3
Answer »Answer: (b)
Using Rule 1,
Speed of truck = 550m/minute
Speed of bus = $33000/45$ m/minute
or $2200/3$ m/minute
Required ratio = 550 : $2200/3$
= $1 : 4/3 = 3 : 4$
Question : 4
Two trains started at the same time, one from A to B and the other from B to A. If they arrived at B and A respectively 4 hours and 9 hours after they passed each other, the ratio of the speed of the two trains was
a) 3 : 2
b) 4 : 3
c) 5 : 4
d) 2 : 1
Answer »Answer: (a)
Using Rule 11,Time taken by 1st man to reach B after meeting 2nd man at C is '$t_1$' and time taken by 2nd man to reach A after meeting 1st man at C is '$t_2$' then:${\text"Speed of 1st man"(s_1)}/{\text"Speed of 2nd man"(s_2)} = √{t_2/t_1}$Distance from A to B = $s_1t_1 + S_2t_2$
Required ratio of the speed of two trains
= $√{9}/√{4} = 3/2$ or 3 : 2
Question : 5
It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the car is :
a) 3 : 4
b) 4 : 3
c) 4 : 5
d) 3 : 5
Answer »Answer: (a)
Let the speed of train be x kmph. and the speed of car be y kmph.
Time = $\text"Distance"/ \text"Speed"$
According to the question,
$120/x + 480/y$ = 8
$15/x + 60/y$ = 1 ...(i)
and, $200/x + 400/y = 25/3$
$8/x + 16/y = 1/3$
$24/x + 48/y$ = 1 ...(ii)
From equations (i) and (ii),
$24/x + 48/y = 15/x + 60/y$
$24/x - 15/x = 60/y - 48/y$
$9/x = 12/y$
$x/y = 9/12 = 3/4$ = 3 : 4
Question : 6
The ratio of length of two trains is 5 : 3 and the ratio of their speed is 6 : 5. The ratio of time taken by them to cross a pole is
a) 11 : 8
b) 25 : 18
c) 27 : 16
d) 5 : 6
Answer »Answer: (b)
Required ratio
= $5/6 : 3/5$
${30 × 5}/6 : {30 × 3}/5$ = 25 : 18
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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