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) 2 hours
(b) 2$2/3$ hours
(c) 1$2/3$ hours
(d) 1$1/3$ hours
The correct answers to the above question in:
Answer: (d)
Ratio of speed = 3 : 4
Ratio of time taken = 4 : 3
Let the time taken by A and B be 4x hours and 3 x hours respectively.
Then, $4x - 3x = 20/60 ⇒ x = 1/3$
Time taken by A = 4x hours
= $(4 × 1/3)$ hours = 1$1/3$ hours
Using Rule 9,
Here, $S_1 = 3x, S_2 = 4x$
$t_2 = y, t_1 = y + 20/60 = y + 1/3$
$S_1t_1 = S_2t_2$
$3x(y + 1/3) = 4xy$
3y + 1 = 4y, y = 1
∴ Time taken by A
= 1 + $1/3 = 1{1}/3$ hours
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Read more problems with ratios Based Quantitative Aptitude Questions and Answers
Question : 1
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
Question : 2
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 : 3
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 : 4
A and B run a 5 km race on a round course of 400 m. If their speed are in the ratio 5 : 4, the number of times, the winner passes the other, is
a) 2
b) 3
c) 5
d) 1
Answer »Answer: (b)
The winner will pass the other, one time in covering 1600m.
Hence, the winner will pass the other 3 times in completing 5km race.
Question : 5
A cyclist, after cycling a distance of 70 km on the second day, finds that the ratio of distance covered by him on the first two days is 4 : 5. If he travels a distance of 42 km. on the third day, then the ratio of distance travelled on the third day and the first day is :
a) 3 : 2
b) 3 : 4
c) 2 : 3
d) 4 : 3
Answer »Answer: (b)
Using Rule 1,
Distance covered on the first day
= $4/5 × 70$ = 56 km
∴ Required ratio = 42 : 56 = 3 : 4
Question : 6
A truck covers a distance of 550 metre in one minute where as a bus covers a distance of 33 km in $3/4$ hour. Then the ratio of their speeds is :
a) 2 : 3
b) 3 : 4
c) 1 : 4
d) 1 : 3
Answer »Answer: (b)
Speed of truck
= ${550\text"metre"}/{60\text"second"} = (55/6)$ m./sec.
Speed of bus
= ${33 × 1000 \text"metre"}/{3/4 × 60 × 60 \text"second"} = 440/36$ m./sec.
∴ Required ratio = $55/6 : 440/36$
= 55 × 6 : 440 = 3 : 4
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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