Model 1 Basic Time & Distance using formula 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 : 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

The correct answers to the above question in:

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.

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Read more basic problems formulas Based Quantitative Aptitude Questions and Answers

Question : 1

The speed 3$1/3$ m/sec when expressed in km/hour becomes

a) 12

b) 10

c) 9

d) 8

Answer: (a)

Since, 1 m/sec = $18/5$ kmph

$10/3$ m/sec

= $18/5 × 10/3$ = 12 kmph

Question : 2

An aeroplane covers a certain distance at a speed of 240 km hour in 5 hours. To cover the same distance in 1$2/3$ hours, it must travel at a speed of :

a) 720 km./hr.

b) 600 km./hr.

c) 360 km./hr.

d) 300 km./hr.

Answer: (a)

Using Rule 1,

Let the required speed is x km/ hr

Then, $240 × 5 = 5/3 × x$

x = 720 km/hr.

Question : 3

The speed of a bus is 72 km/hr. The distance covered by the bus in 5 seconds is

a) 74.5 m

b) 50 m

c) 60 m

d) 100 m

Answer: (d)

Using Rule 1,

Speed of bus = 72 kmph

= $({72 × 5}/18)$ metre/second

= 20 metre/second

∴ Required distance

= 20 × 5 = 100 metre

Question : 4

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: (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 : 5

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: (c)

Using Rule 1,

Remaining time

= $2/5 × 15 = 6$ hours

Required speed

= $60/6$ = 10 kmph

Question : 6

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: (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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