time and distance Model Questions & Answers, Practice Test for ssc mts tier 1 2024

Question :1

The ratio of speeds of X and Y is 5 : 6. If Y allows X a start of 70 m in a 1.2 km race, then who will win the race and by what distance ?

Answer: (a)

Let us assume that speed of X = 5m/s

∴ speed of Y = 6m/s

Time taken by Y to cover 1.2 km race

$t_Y = {1200}/6$ = 200sec

Time taken by X to cover 1.2 km race

$t_X = {1200 – 70}/5 = {1130}/5$ = 226sec

So Y wins the race by 26 sec.

Distance travelled by X in

26 sec = 26 × 5 = 130 m

Question :2

A bike consumes 20 mL of petrol per kilometre, if it is diriven at a speed in the range of 25 – 50 km/hour and consume 40 mL of petrol per kilometer at any other speed. How much petrol is consumed by the bike in travelling distance of 50 km, if the bike is driven at a speed of 40 km/ hour for the first 10 km, at a speed of 60 km/hour for the next 30 km and at a speed of 30 km/hour for the last 10 km?

Answer: (d)

Speed of bike = 25 – 50 km/h

Consumption of petrol at 25-50 hm/hr = 20 ml/km

and consumes petrol = 40 ml/km at other speed

Given Distance

50km → 10 km + 30 km + 10 km

Speed → 40 km/hr 60 km/hr 30 km/hr

Petrol consumed = (10 + 10) × 20 ml + 30 × 40 ml

= 400 ml + 1200 ml

= 1600 ml

= ${1600}/{100}$ L = 1.6L

∴ Option (d) is correct.

Question :3

A car moves 300 km at a speed of 45 kmph and then it increases its speed to 60 kmph to travel another 500 km. Find average speed of car.

Answer: (a)

Total distance covered = 300 + 500 = 800 km.

Total time taken to cover 800 km

= $300/45+500/60=20/3+25/3=45/3$=15hr.

∴ Average speed = $800/15=160/3=53{1/3}$ kmph

Question :4

The speeds of three cars are in the ratio 2: 3 :4. What is the ratio between the times taken by these cars to travel the same distance ?

Answer: (d)

When speed ratio is $S_1 : S_2 : S_3 : S_4$

than time ratio will be $1/{S_1} : 1/{S_2} : 1/{S_3} : 1/{S_4}$ ...

i.e. time ratio $1/2 : 1/3 : 1/4$

⇒6 : 4 : 3

Question :5

The wheels of a car are of diameter 80cm each. The car is travelling at a speed of 66 Km/hour. What is the number of complete revolutions each wheel makes in 10 minutes ?

Answer: (a)

Radius of wheels = ${80}/2$ cm = 40 cm

Wheel covers in 1 revolution = 2πr = 2 × ${22}/7$ × 40

Speed of wheel = 66 km/hr or

${66 × 1000 × 100 cm}/{60 min}$

Distance covered in 10 minutes

= ${66 × 1000 × 100 × 10}/{60}$

No. of revolution = ${66 × 1000 × 100 × 10}/{60 × 2 × 22 × 40}$ × 7 = 4375

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