Model 2 Vehicles in x/y of its usual speed Practice Questions Answers Test with Solutions & More Shortcuts

Question : 1 [SSC CGL Tier-I 2016]

A car covers a certain distance in 25 hours. If it reduces the speed by $1/5$th, the car covers 200 km. less in that time. The speed of car is

a) 50 km./hr.

b) 40 km./hr.

c) 30 km./hr.

d) 60 km./hr.

Answer: (b)

Speed of car = x kmph.

Distance = Speed × Time = 25x km.

Case II,

Speed of car = ${4x}/5$ kmph.

Distance covered

= ${4x}/5 × 25$ = 20x km.

According to the question,

25x - 20x = 200

5x = 200

x = $200/5$ = 40 kmph.

Question : 2 [SSC CGL Tier-II 2015]

A car covers four successive 7 km distances at speeds of 10 km/hour, 20 km/hour, 30 km/ hour and 60 km/hour respectively. Its average speed over this distance is

a) 40 km/hour

b) 60 km/hour

c) 20 km/hour

d) 30 km/hour

Answer: (c)

Total distance

= 7 × 4 = 28 km.

Total time

= $(7/10 + 7/20 + 7/30 + 7/60)$ hours

= $({42 + 21 + 14 + 7}/60)$ hours

= $84/60$ hours = $7/5$ hours

Average speed

= $\text"Total distance"/ \text"Total time" = (28/{7/5})$ kmph

= ${28 × 5}/7$ = 20 kmph

Question : 3 [SSC CGL Tier-1 2011]

Walking at $3/4$ of his usual speed, a man is 1$1/2$ hours late. His usual time to cover the same distance, (in hours) is

a) 5

b) 5$1/2$

c) 4

d) 4$1/2$

Answer: (d)

Time and speed are inversely proportional.

$4/3$ of usual time –usual time = $3/2$

$1/3$ usual time = $3/2$

Usual time = ${3 × 3}/2$

$9/2 = 4{1}/2$ hours

Using Rule 8,

Here, A = 3, B = 4, t= $3/2$

Usual time = $\text"A"/\text"Diff of A and B"$ × time

= $3/{(4 - 3)} × 3/2 = 4{1}/2$ hrs.

Question : 4 [SSC CHSL 2015]

A car goes 20 metres in a second. Find its speed in km/hr.

a) 20

b) 36

c) 72

d) 18

Answer: (c)

1 m/sec = $18/5$ kmph

20 m/sec = ${20 × 18}/5$

= 72 kmph

Question : 5 [SSC CGL Prelim 2005]

A car travelling with $5/7$ of its usual speed covers 42 km in 1 hour 40 min 48 sec. What is the usual speed of the car?

a) 30 km/hr

b) 25 km/hr

c) 35 km/hr

d) 17$6/7$ km/hr

Answer: (c)

1 hr 40 min 48 sec

= 1 hr $(40 + 48/60)$ min

= 1 hr $(40 + 4/5)$ min

= 1 hr $204/5$ min

= $(1 + 204/300)$ hr = $504/300$ hr

Speed = $42/{504/300}$ = 25 kmph

Now, $5/7$ usual speed = 25

Usual speed = ${25 × 7}/5$ = 35 kmph

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