Bissoy.com
Doctors Medicines MCQs Q&A

A bus moves from station A towards station B, which is at a distance of 189 km. An hour later, a car, the ratio of whose speed with the bus is 3 ∶ 2, starts from station A and moves towards station B. Find the speed of the bus (in km/h), if the car arrives at station B in half an hour earlier than the bus. 

A bus moves from station A towards station B, which is at a distance of 189 km. An hour later, a car, the ratio of whose speed with the bus is 3 ∶ 2, starts from station A and moves towards station B. Find the speed of the bus (in km/h), if the car arrives at station B in half an hour earlier than the bus.  Correct Answer 42

Given:

Distance = 189 km

The ratio of the speed of car and bus = 3 : 2

Concept used:

When the distance is constant, then speed is inversely proportional to time

Formula used:

Speed = Distance/Time

Calculation:

The ratio of speed of car and bus be 3x and 2x respectively

When the distance is constant, then speed is inversely proportional to time

So,

The ratio of time of car and bus be 2x and 3x respectively

Now,

The difference between the time of bus and car = (3x – 2x) = 1x

According to the question

Total time taken by car = (60 min + 30 min) = 90 min

⇒ (90/60) = 3/2 hr

Time taken by bus = (3 × 3/2) = 9/2 = 4.5 hr 

Now,

Speed = 189/4.5

⇒ 42 km/h

∴ The speed of the bus is 42 km/h

Confusing point:

Time taken by car to move from station A to station B firstly by one hour and then extra half an hour.

Related Questions

Each of the question below consists of a question and three statements number I, II and III given below it. You have to decide whether the data provided in the statement are sufficient to answer the question. If the bus is travelling from Surat to Ahmadabad and a car is travelling from Ahmadabad to Surat, then what is the distance between Surat and Ahmadabad? I. The speed of a car is 40% less than the speed of bus. Bus started at 9 am and car started at 10 am and they meet at 3 pm of the same day. II. After travelling for 1 hour, because of traffic average speed of bus is decreased by 20% and covers distance between Surat to Ahmadabad in 11 hours. Original speed of car is 20% less than original speed of bus and before crossing bus it covered 200 km if starts 1 hour later than bus. After crossing car, bus covers remaining distance in 5 hours. III. Speed of bus is 10 km/hr more than the speed of car and before crossing car ratio of distances covered bus and car in same time was 5 : 4. Time taken by car to cover the distance between Ahmadabad and Surat is 2 hours 15 minutes more than time taken by bus to cover the same distance.
Three cars start from point A together and reach point B at equal intervals. Second car whose sped is less than third car but more than first car taken a u turn and starts its journey towards A whereas third car heads for point C which is 100 km away from point B. First car and third car meet each other at mid way of A and C after third car takes u turn from C. First car travels half the distance between A and B when second reaches B. The sum of speed of second car and third car is 100 kmh.  What is the difference between speed of third car and first car?
The question below is followed by three statements I, II, and III. You have to determine whether the data given is sufficient for answering the question. You should use the data and your knowledge of mathematics to choose the best possible answer. A car travels from city P to city Q in T hours with a speed of v km per hour. Distance between cities P and Q is D kilometers. If it increases its speed by 5 kmph it saves some time. Find the actual speed of the car. Statement I: If the car travels from P to Q with its actual speed of v kmph and come back with the speed of v + 5 kmph in 2T – 0.6 hrs Statement II: A bus start form Q at the same time when the car starts from P and the speed of the bus is 50% more than the speed of the car and the bus meets car after covering 60% of the distance Statement III: Distance between PQ is given by D2 – 25D + 200 = 0  
Gaurav cycles towards South-West for a distance of 6 m and stops there. Further, he moves towards East a distance of 10 m and from there he moves towards North-East a distance of 6 m. Next, he moves towards West a distance of 6 m. Now, he moves towards North-West a distance of 2 m. Next, he moves towards West a distance of 4 m and then towards South-West 6 m and stops at that point. Now, where is he from the starting point?
A computer has 1000K of main memory. The jobs arrive and finish in the following sequence. Job 1 requiring 200 K arrives Job 2 requiring 350 K arrives Job 3 requiring 300 K arrives Job 1 finishes Job 4 requiring 120 K arrives Job 5 requiring 150 K arrives Job 6 requiring 80 K  arrives Among best fit and first fit, which performs better for this sequence?
The distance between two bus stops of Bhopal and Jabalpur is 390 km. A bus starts from bhopal and moves towards Jabalpur at an average speed of 24 km/h. Another bus starts from Jabalpur, 15 minutes earlier than the first bus and moves towards bhopal at an average speed of 30 km/h. How far from Jabalpur will the two buses will meet respectively:
Study the two cases and answer in terms of relation between the two cases Case 1: The average speed of the bike is \(3\frac{3}{4}\) times the average speed of the bus. A car covers 720 km in 10 hours. How much distance (in km) will a bike cover in 50 minutes if the speed of the bus is half of the speed of the car? Case 2: The average speed of bike is \(1\frac{2}{5}\) times the average speed of the car. A bus covers 441 km in 7 hours. How much distance (in km) will a bike cover in 45 minutes if the speed of the car is twice the speed of the bus?
The distance between two station A and B is 1000 km. A train starts from A and moves towards B at an average speed of 60 km/hr. Another train starts from B, 2 hours later than the train from A, and moves towards A at an average speed of 50 km/hr. When will the two trains cross each other after A starts journey?
Car A starts its journey from P to Q simultaneously another car Y starts from point Q to P and both reach their destination in 3 hours. Car A travels with a speed of 50 km/hr for first hour, 60 km/hr for second hour and 70 km/hr for third hour. Car B travels with 70 km/hr in first hour, 40 km/hr in second hour and 70 km/hr in third hour. After how much time they will meet, if they both start at the same time?
Two cities M and N are 1000 km apart. Car A starts from City M towards City N and Car B starts from City N towards City M at the same time. Car B caused some malfunction and idle for some time. The ratio of the distance between the meeting point to City M and the distance between the meeting point to City N is 3 : 2. The ratio between their speeds is in the ratio 4 : 5. If the idle time was 2 hrs, what is the speed of Car B?