CAT Algebra

Reading Test 1

Question No : 1

Q.1 A car travels at 30 km/h for the first 2 hours of a journey and then travels at 40 km/h for the next 2 hours of the journey. Find the ratio of the distance travelled at the two speeds.

Question No : 2

Q.2 Two cars leave simultaneously from points A and B on a straight line towards each other. The distance between A and B is 100 km. They meet at a point 40 kms from A. Find the ratio of their speeds.

Question No : 3

Q.3 Two cars move simultaneously from points A and B towards each other. The speeds of the two cars are 20 m/s and 25 m/s respectively. Find the meeting point if d(AB) = 900 km.

Question No : 4

Q.4 A train meets with an accident and moves at 3/4 its original speed. Due to this, it is 20 minutes late. Find the original time for the journey beyond the point of the accident.

Question No : 5

Q.5 A man travels from his house to his office at 5 km/h and reaches his office 20 minutes late. If his speed has been 7.5 km/h, he would have reached his office 12 minutes early. Find the distance from his house to his office.

Question No : 6

Q.6 A body travels half the journey at 20 kmph and the other half at 30 kmph. Find the average speed.

Question No : 7

Q.7 Two bodies A and B start from opposite ends P and Q of a straight road. They meet at a point 0.6D from P. Find the point of their fourth meeting.

Question No : 8

Q.8 A starts walking from a place at a uniform speed of 2 km/h in a particular direction. After half an hour, B starts from the same place and walks in the same direction as A at a uniform speed and overtakes A after 1 hour 48 minutes. Calculate the speed of B.

Question No : 9

Q.9 Water flows into a cylindrical beaker at a constant rate. The base area of the beaker is 24 cm². The water level rises by 10 cm every second. How quickly will the water level rise in a beaker with a base area of 30 cm²?

Question No : 10

Q.10 A 2 kilowatt heater can boil a given amount of water in 10 minutes. How long will it take for a less powerful heater of 1.2 kilowatts to boil the same amount of water?

Question No : 11

Q.11 A 2 kilowatt heater can boil a given amount of water in 10 minutes. How long will it take for a less powerful heater of 1.2 kilowatts to boil double the amount of water?

Question No : 12

Q.12 A car travels at 60 km/h from Mumbai to Poona and at 120 km/h from Poona to Mumbai. What is the average speed of the car for the entire journey?

Question No : 13

Q.13. A train crosses a pole in 8 seconds. If the lenght of the train is 200 meters, find the speed of the train.

Question No : 14

Q.14 A train crosses a man travelling in another train in the opposite direction in 8 seconds. However, the train requires 25 seconds to cross the same man if the trains are travelling in the same direction. If the length of the first train is 200 metres and that of the train in which the man is sitting is 160 metres, find the speed of the frst train.

Question No : 15

Q.15 At what time between 2-3 p.m. is the first right angle in that time formed by the hands of the clock?

Question No : 16

Q.16 The Sinhagad Express left Pune at noon sharp. Two hours later, the Deccan Queen started from Pune in the same direction. The Deccan Queen overtook the Sinhagad Express at 8 p.m. Find the average speed of the two trains over this journey if the sum of their average speeds is 70 km/h.