Model 4 Time & Distance with Ratios Section-Wise Topic Notes With Detailed Explanation And Example Questions

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The following question based on time & distance topic of quantitative aptitude

Questions : The speed of two trains are in the ratio 6 : 7. If the second train runs 364 km in 4 hours, then the speed of first train is

(a) 72 km/hr

(b) 78 km/hr

(c) 84 km/hr

(d) 60 km/hr

The correct answers to the above question in:

Answer: (b)

Using Rule 1,
Distance = Speed × Time
Speed = $\text"Distance"/\text"Time"$ , Time = $\text"Distance"/\text"Speed"$
1 m/s = $18/5$ km/h, 1 km/h = $5/18$ m/s

Speed of second train

= $364/4$ = 91 kmph

7x ≡ 91

6x ≡ $91/{7x}$ × 6x ≡ 78 kmph

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Read more problems with ratios Based Quantitative Aptitude Questions and Answers

Question : 1

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: (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 : 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: (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

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: (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

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