AILET entrance exam Question Bank Solutions for Mathematics

A man covered a certain distance at some speed. Had he moved 3 km/h faster, he would have taken 40 min less. If he had moved 2 km/h slower, he would have taken 40 min more. The distance (in km) is

In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/h and the time of flight increased by 30 min. The duration of the flight is

Excluding stoppages, the speed of a bus is 54 km/h and including stoppages, it is 45 km/h. For how many minutes does the bus stop per hour?

Robert is travelling on his cycle and has calculated to reach point A at 2 pm if he travels at 10 km/h, he will reach there at 12 noon if he travels at 15 km/h. At what speed must he travel to reach A at 1 pm?

The length of the bridge, which a train 130 m long on travelling at 45 km/h can cross in 30 s, is

A train passes a 110 m long platform in 40 s and a boy standing on the platform in 30 s. The length of the train is

A train moving with uniform speed crosses a pole in 2 s and a 250 m long bridge in 7 s. Find the length of the train.

Two trains, each 100 m long, moving in opposite directions, cross each other in 8 s. If one is moving twice as fast the other, then the speed of the faster train is

Two trains of equal length are running on parallel lines in the same direction at 46 km/h and 36 km/h. The faster train passes the slower train in 36 s. The length of each train is

Two trains running in opposite directions cross a man standing on the platform in 27 sec and 17 sec, respectively and they cross each other in 23 sec. The ratio of their speeds is

A train can travel 50% faster than a car. Both start from point A at the same time and reach point B which is 75 km away from A at the same time. On the way. however, the train lost about 12.5 min while stopping at the stations. The speed of the car is

A boat takes 90 min less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 m/h, the speed of the stream is

A man rows to a place 48 km distance and come back in 14 h. He finds that he can row 4 km with the stream at the same time as 3 km against the stream. The rate of the stream is

A boat running upstream takes 8 h 48 m to cover a certain distance, while it takes 4 h to cover the same distance running downstream. What is the ratio between the speed of the boat and the speed of the water current respectively?

Mr. X drives to his office at an average speed of 48 km per hour. The time taken to cover the first 60% of the distance is 10 minutes more than the time taken to cover the remaining distance. How far is his office?

A car completes a certain journey in 8 h. It covers half the distance at 40 km/h and the rest at 60 km/h. The length of the journey is

A man covers half of his journey as 6 km/h and the remaining half at 3 km/h. His average speed is

A goods train is 800 meters long and it is running at a constant speed of 60 km/per hour. If it takes 120 seconds to pass a bridge, then calculate the length of the bridge?

It takes eight hours for a 600 km journey. if 120 km is done by train and the rest by car. It takes 20 min more if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is

Find the number of real solutions for the equation `(8^x + 27^x)/(12^x + 18^x) = 7/6`.