Speed, Time & Distance Practice MCQs (Chapter-7): 100 Important Questions for Quantum Aptitude Preparation

Explanation:

In 6 hours, the car would have traveled 90 km/h × 6 h = 540 km. In the same 6 hours, the motorcycle would have traveled 60 km/h × 6 h = 360 km. Since the motorcycle started 2 hours later, it would have covered 360 km - (60 km/h × 2 h) = 360 km - 120 km = 240 km less than the car. Therefore, the distance between them is 240 km + 360 km = 600 km.

Explanation:

To find the total time, add the time spent traveling and the time spent stopped) Time spent traveling = Distance / Speed = 240 km / 80 km/h = 3 hours. Adding the 30 minutes (0.5 hours) stop time gives a total of 3 hours + 0.5 hours = 4 hours.

Explanation:

The speed of the boat in still water can be calculated as Boat Speed = (Downstream Speed - Stream Speed) = (48 km/h - 8 km/h) = 40 km/h.

Explanation:

To find the time for the round trip, you can use the formula: Time = Distance / Speed) The one-way trip from X to Y takes 120 km / 60 km/h = 2 hours, and the return trip takes 120 km / 45 km/h = 2.67 hours (approximately). The total time is approximately 2 hours + 2.67 hours ≈ 4 hours.

Explanation:

Time taken by the bus = Distance / Bus Speed = 300 km / 50 km/h = 6 hours. Time taken by the car = Distance / Car Speed = 300 km / 75 km/h = 4 hours. The car saves 6 hours - 4 hours = 2 hours compared to the bus.

Explanation:

The average speed for a round trip can be calculated using the formula: Average Speed = (2 × Speed1 × Speed2) / (Speed1 + Speed2). In this case, Average Speed = (2 × 80 km/h × 100 km/h) / (80 km/h + 100 km/h) = 16000/180 = 88.88 km/h (approximately 88 km/h).

Explanation:

To find the average speed for the round trip, use the formula: Average Speed = (2 × Speed1 × Speed2) / (Speed1 + Speed2) = (2 × 20 km/h × 30 km/h) / (20 km/h + 30 km/h) = (1200 km/h²) / (50 km/h) = 24 km/h.

Explanation:

First, convert the speed to m/s by multiplying by 1000/3600 (since 1 km/h = 1000/3600 m/s). So, Speed = (50 km / 2.5 hours) × (1000/3600) = 6 m/s.

Explanation:

Time can be calculated using the formula: Time = Distance / Speed) In this case, Time = 12 km / 4 km/h = 3 hours.

Explanation:

To calculate the distance traveled, you can use the formula: Distance = Speed × Time. In this case, Distance = 60 km/h × 3 hours = 180 km.

Explanation:

Speed is calculated using the formula: Speed = Distance / Time. In this case, Speed = 300 km / 5 hours = 60 km/h.

Explanation:

First, convert the distance from miles to kilometers because the speed is in km/h. 1 mile = 1.60934 km. So, Distance = 250 miles × 1.60934 km/mile ≈ 402.34 km. Now, use the formula: Time = Distance / Speed = 402.34 km / 100 km/h = 4.0234 hours ≈ 2.5 hours (rounded to the nearest half-hour).

Explanation:

Let the speed of the current be "C" km/h and the person's speed in still water be "S" km/h. When swimming downstream, the effective speed is (S + c) km/h, and when swimming upstream, it's (S - c) km/h.
Given that downstream takes 3 hours to cover 30 km, we have the equation: (S + c) × 3 = 30. Solving for S + C, we get S + C = 10.
Given that upstream takes 6 hours to cover 30 km, we have the equation: (S - c) × 6 = 30. Solving for S - C, we get S - C = 5.
Now, we have a system of equations:
S + C = 10
S - C = 5
Adding these equations gives us 2S = 15, so S = 7.5 km/h. Substituting this into equation 1 gives us C = 10 - 7.5 = 2.5 km/h. Therefore, the speed of the current is 2.5 km/h, and the person's speed in still water is 7.5 km/h.