TRAIN AND DISTANCE

1. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

A. 120 metres B. 180 metres C. 324 metres D. 150 metres

2. A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:

A. 45 km/hr B. 50 km/hr C. 54 km/hr D. 55 km/hr

3. The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:

A. 200 m B. 225 m C. 245 m D. 250 m

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

A. 1 : 3 B. 3 : 2 C. 3 : 4 D. None of these

5. A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

A. 120 m B. 240 m C. 300 m D. None of these

6. A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?

A. 65 sec B. 89 sec C. 100 sec D. 150 sec

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

A. 50 m B. 72 m C. 80 m D. 82 m

8. A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?

A. 40 sec B. 42 sec C. 45 sec D. 48 sec

9. Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:

A. 36 B. 45 C. 48 D. 49

10. A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger? A. 3.6 sec B. 18 sec C. 36 sec D. 72 sec

11. A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?

A. 230 m B. 240 m C. 260 m D. 320 m E. None of these

12. A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?

A. 230 m B. 240 m C. 260 m D. 270 m

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

A. 30 km/hr B. 45 km/hr C. 60 km/hr D. 75 km/hr

14. Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:

A. 9 B. 9.6 C. 10 D. 10.8

15. A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?

A. 5 sec B. 6 sec C. 7 sec D. 10 sec

16. A train travelling at a speed of 75 mph enters a tunnel 3 miles long. The train is mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?

A. 2.5 min B. 3 min C. 3.2 min D. 3.5 min

17. A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is:

A. 130 B. 360 C. 500 D. 540

18. A 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds.

What is the length of the platform?

A. 320 m B. 350 m C. 650 m D. Data inadequate

19 A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:

A. 50 m B. 150 m C. 200 m D. Data inadequate

20. A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train? A. 69.5 km/hr B. 70 km/hrC. 79 km/hr D. 79.2 km/hr

21. How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?

A. 25 B. 30 C. 40 D. 45

22. Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.

A. 12 sec B. 24 sec C. 48 sec D. 60 sec

23. Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:

A. 10 B. 18 C. 36 D. 72

24. Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?

A. 10 B. 12 C. 15 D. 20

25. A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is: A. 48 km/hr B. 54 km/hr C. 66 km/hr D. 82 km/hr

27. A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:

A. 45 m B. 50 m C. 54 m D. 72 m

28.A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?

A. 66 km/hr B. 72 km/hr C. 78 km/hr D. 81 km/hr

29. A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is

A. 400 m B. 450 m C. 560 m D. 600 m

30. Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?

A. 9 a.m. B. 10 a.m. C. 10.30 a.m. D. 11 a.m.

PROBLEMS ON AGES

1. Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit's age. After further 8 years, how many times would he be of Ronit's age?

A.2 times B. 2.5 times C. 2 3/4 times D. 3 times

2. The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?

A. 4 years B. 8 years C. 10 years D. None of these

3. A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:

A. 14 years B. 19 years C. 33 years D. 38 years

4. A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B?

A. 7 B. 8 C. 9 D. 10 E. 11

5. Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?

A. 24 B. 27 C. 40 D. Cannot be determined E. None of these

6. A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:

A. 14 years B. 18 years C. 20 years D. 22 years

7. Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?

A.16 years B.18 years C.20 years D.Cannot be determined E.None of these

8. The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:

A. 12 years B. 14 years C. 18 years D. 20 years

9. At present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present ?

A. 12 years B. 15 years C. 19 and half D. 21 years

10. Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?

A.16 years B.18 years C. 28 years D.24.5 years E.None of these

11. The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).

A. 8, 20, 28 B. 16, 28, 36 C. 20, 35, 45 D. None of these

12. Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?

A. 2 years B. 4 years C. 6 years D. 8 years

13.A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?

A. 32 years B. 36 years C. 40 years D. 48 years

14. Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q's age?

A. 1 year B. 2 years C. 25 years D.Data inadequate E. None of these

15. The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is:

A. 5 : 2 B. 7 : 3 C. 9 : 2 D. 13 : 4.

PROBLEMS ON AVERAGE

1. In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?

A. 6.25 B. 6.5 C. 6.75 D. 7

2. A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?

A. 28 4/7 years B. 31 5/7 years C. 32 1/7 years D. None of these

3. A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?

A. Rs. 4991 B. Rs. 5991 C. Rs. 6001 D. Rs. 6991

4. The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?

A. 0 B. 1 C. 10 D. 19

5.The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?

A. 76 kg B. 76.5 kg C. 85 kg D. Data inadequate E. None of these.

6. The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?

A. 23 years B. 24 years C. 25 years D. None of these

7. The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is:

A. 3500 B. 4000 C. 4050 D. 5000

8. The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:

A. 35 years B. 40 years C. 50 years D. None of these

9. A car owner buys petrol at Rs.7.50, Rs. 8 and Rs. 8.50 per litre for three successive years. What approximately is the average cost per litre of petrol if he spends Rs. 4000 each year?

A. Rs. 7.98 B. Rs. 8 C. Rs. 8.50 D. Rs. 9

10. In Arun's opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Arun?

A. 67 kg. B. 68 kg. C. 69 kg. D. Data inadequateE. None of these

11. The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:

A. 17 kg B. 20 kg C. 26 kg D. 31 kg

12. The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.

A. 47.55 kg B. 48 kg C. 48.55 kg D. 49.25 kg

13. A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:

A. 250 B. 276 C. 280 D. 285

14. If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is:

A. 53.33 B. 54.68 C. 55 D. None of these

15. A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half (1/2). The number of pupils in the class is:

A. 10 B. 20 C. 40 D. 73

TIME AND DISTANE

1. A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?

A. 3.6 B. 7.2 C. 8.4 D. 10

2. An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 hours, it must travel at a speed of:

A. 300 kmph B. 360 kmph C. 600 kmph D. 720 kmph

3. If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is:

A. 50 km B. 56 km C. 70 km D. 80 km

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

A. 100 kmph B. 110 kmph C. 120 kmph D. 130 kmph

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

A. 9 B. 10 C. 12 D. 20

6. 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/hr and the time of flight increased by 30 minutes. The duration of the flight is:

A. 1 hour B. 2 hours C. 3 hours D. 4 hours

7. A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.

A. 220 km B. 224 km C. 230 km D. 234 km

8. The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is:

A. 70 km/hr B. 75 km/hr C. 84 km/hr D. 87.5 km/hr

9. A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:

A. 35.55 km/hr B. 36 km/hr C. 71.11 km/hr D. 71 km/hr

10. A car travelling with 5/7 of its actual speed covers 42 km in 1 hr 40 min 48 sec. Find the actual speed of the car.

A. 17 6/7 km/hr B. 25 km/hr C. 30 km/hr D. 35 km/hr

11. In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:

A. 5 kmph B. 6 kmph C. 6.25 kmph D. 7.5 kmph

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

A. 8 kmph B. 11 kmph C. 12 kmph D. 14 kmph

13. It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes 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:

A. 2 : 3 B. 3 : 2 C. 3 : 4 D. 4 : 3

14. A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot @ 4 km/hr and partly on bicycle @ 9 km/hr. The distance travelled on foot is:

A. 14 km B. 15 km C. 16 km D. 17 km

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

A. 35 B. 36 2/3 C. 37.5 D. 40.

HEIGHT AND DISTANCE

1. Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:

A. 173 m B. 200 m C. 273 m D. 300 m

2. A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30º with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60º. What is the distance between the base of the tower and the point P?

A. 43 units B. 8 units C. 12 units D. Data inadequate E. None of these

3. The angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:

A. 2.3 m B. 4.6 m C. 7.8 m D. 9.2 m

4. An observer 1.6 m tall is 20√3 away from a tower. The angle of elevation from his eye to the top of the tower is 30º. The heights of the tower is:

A.21.6 m B.23.2 m C. 24.72 m D. None of these

5. From a point P on a level ground, the angle of elevation of the top tower is 30º. If the tower is 100 m high, the distance of point P from the foot of the tower is:

A. 149 m B. 156 m C. 173 m D. 200 m.

6. The angle of elevation of the sun, when the length of the shadow of a tree √3 times the height of the tree, is:

A. 30º B. 45º C. 60º D. 90º

SIMPLE INTEREST

1. A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:

A. Rs. 650 B. Rs. 690 C. Rs. 698 D. Rs. 700

2. Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B?

A. Rs. 6400 B. Rs. 6500 C. Rs. 7200 D. Rs. 7500 E. None of these

3. A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?

A. Rs. 4462.50 B. Rs. 8032.50 C. Rs. 8900 D. Rs. 8925 E. None of these

4. How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?

A. 3.5 years B. 4 years C. 4.5 years D. 5 years

5. Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?

A. 3.6 B. 6 C. 18 D. Cannot be determined E. None of these

6. A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest?

A. 3% B. 4% C. 5% D. 6% E. None of these

7. A person takes a loan of Rs. 200 at 5% simple interest. He returns Rs. 100 at the end of 1 year. In order to clear his dues at the end of 2 years, he would pay:

A. Rs. 105 B. Rs. 110 C. Rs. 115 D. Rs. 115.50

8. An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes:

A. 10% B. 10.25% C. 10.5% D. None of these

9. A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is:

A. 5% B. 7% C. 7 1/8 % D. 10%

10. A sum of Rs. 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What was the original rate of interest?

A. 3.6% B. 4.5% C. 5% D. 6% E.None of these

11. A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:

A. Rs. 2000 B. Rs. 10,000 C. Rs. 15,000 D. Rs. 20,000

12. A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is:

A. 5% B. 8% C. 12% D. 15%

13.What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years?

A. 1 : 3 B. 1 : 4 C. 2 : 3 D. Data inadequate

14. A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?

A. Rs. 35 B. Rs. 245 C. Rs. 350 D. Cannot be determined E. None of these

15. A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6 p.a for 2 years. Find his gain in the transaction per year.

A. Rs. 112.50 B. Rs. 125 C. Rs. 150 D. Rs. 167.50

PROFIT AND LOSS

1.Alfred buys an old scooter for Rs. 4700 and spends Rs. 800 on its repairs. If he sells the scooter for Rs. 5800, his gain percent is:

A. 4 4/7% B.5 5/11 % C. 10% D. 12%

2. The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:

A. 15 B. 16 C. 18 D. 25

3. If selling price is doubled, the profit triples. Find the profit percent.

A. 66 2/3 B. 100 C 105 1/ 3 D. 120

4. In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?

A. 30% B. 70% C. 100% D. 250%

5. A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?

A. 3 B. 4 C. 5 D. 6

6. The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?

A. Rs. 2000 B. Rs. 2200 C. Rs. 2400 D. Data inadequate

7. A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 392, what was his profit?

A. Rs. 18.20 B. Rs. 70 C. Rs. 72 D. Rs. 88.25

8. A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the cycle?

A. Rs. 1090 B. Rs. 1160 C. Rs. 1190 D. Rs. 1202

9. Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?

A. 3.5 B. 4.5 C. 5.6 D. 6.5

10. Some articles were bought at 6 articles for Rs. 5 and sold at 5 articles for Rs. 6. Gain percent is:

A. 30% B. 33 1/3 % C. 35% D. 44%

PERMUTATION AND COMBINATION

1. From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

A. 564 B. 645 C. 735 D. 756 E. None of these

2. In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?

A. 360 B. 480 C. 720 D. 5040 E. None of these

3. In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?

A. 810 B. 1440 C. 2880 D. 50400 E. 5760

4. Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

A. 210 B. 1050 C. 25200 D. 21400 E. None of these

5. In how many ways can the letters of the word 'LEADER' be arranged?

A. 72 B. 144 C. 360 D. 720 E. None of these

6. In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?

A. 159 B. 194 C. 205 D. 209 E. None of these

7. How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?

A. 5 B. 10 C. 15 D. 20

8. In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?

A. 266 B. 5040 C. 11760 D. 86400 E. None of these

9. A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?

A. 32 B. 48 C. 64 D. 96 E. None of these

10. In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?

A. 32 B. 48 C. 36 D. 60 E. 120

11. In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?

A. 63 B. 90 C. 126 D. 45 E. 135

12. How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?

A. 40 B. 400 C. 5040 D. 2520

13. In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?

A. 10080 B. 4989600 C. 120960 D. None of these

14. In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?

A. 120 B. 720 C. 4320 D. 2160 E. None of these.

CHAIN RULE

1. 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?

A. 9 B. 10 C. 11 D. 12

3. Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

A. 648 B. 1800 C. 2700 D. 10800

4. A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:

A. 29 1/5 B. 37¼ C. 42 D. 54

5. 39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?

A. 10 B. 13 C. 14 D. 15

6. A man completes of a job in 10 days. At this rate, how many more days will it takes him to finish the job?

A. 5 B. 6 C. 7 D.7 1/2

7. If a quarter kg of potato costs 60 paise, how many paise will 200 gm cost?

A. 48 paise B. 54 paise C. 56 paise D. 72 paise

8. In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk?

A. 1 B. 1/40 C. 40 D. 80

9. A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:

A. 4 B. 9 C. 12 D. 49

10. If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days?

A. 1 B. 7/2 C. 7 D. 49

11. A flagstaff 17.5 m high casts a shadow of length 40.25 m. The height of the building, which casts a shadow of length 28.75 m under similar conditions will be:

A. 10 m B. 12.5 m C. 17.5 m D. 21.25 m

12. In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal?

A. 20 B. 30 C. 40 D. 50

13. An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 25 metres of cloth?

A. 178 B. 195 C. 204 D. 488

14. 36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?

A. 12 B. 18 C. 22 D. 24 E. None of these

15. 4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?

A. 4 B. 8 C. 12 D. 16

H.F.C AND L.C.M

1. Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.

A. 4 B. 7 C. 9 D. 13

2. The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:

A. 276 B. 299 C. 322 D. 345

3. Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?

A. 4 B. 10 C. 15 D. 16

4. Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:

A. 4 B. 5 C. 6 D. 8

5. The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:

A. 9000 B. 9400 C. 9600 D. 9800

6. The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:

A. 101 B. 107 C. 111 D. 185

7. Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is:

A. 40 B. 80 C. 120 D. 200

8. The G.C.D. of 1.08, 0.36 and 0.9 is:

A. 0.03 B. 0.9 C. 0.18 D. 0.108

9. The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:

A. 1 B. 2 C. 3 D. 4

10. The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is:

A. 74 B. 94 C. 184 D. 364

11. Find the lowest common multiple of 24, 36 and 40.

A. 120 B. 240 C. 360 D. 480

12. The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is:

A. 3 B. 13 C. 23 D. 33

14. The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:

A. 1677 B. 1683 C. 2523 D. 3363

15. A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and c in 198 seconds, all starting at the same point. After what time will they again at the starting point ?

A. 26 minutes and 18 seconds B. 42 minutes and 36 seconds

C. 45 minutes D. 46 minutes and 12 seconds

21. The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is:

A. 15 cm B. 25 cm C. 35 cm D. 42 cm

22. Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is:

A. 75 B. 81 C. 85 D. 89

23. Find the highest common factor of 36 and 84.

A. 4 B. 6 C. 12 D. 18

24. Which of the following fraction is the largest ?

A. 7/8 B. 13/16 C. 31/40 D.63/80

25. The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is:

A. 504 B. 536 C. 544 D. 548

26. The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is:

A. 123 B. 127 C. 235 D. 305

27. Which of the following has the most number of divisors?

A. 99 B. 101 C. 176 D. 182

28. The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then sum of the number is:

A. 28 B. 32 C. 40 D. 64

29. The H.C.F. of 9/10, 12/25, 18/35 and 21/40 is:

A. 3/5 B.252/5 C. 3/1400 D. 63/700

700

30. If the sum of two numbers is 55 and the H.C.F. and L.C.M. of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to:

A. 55/601 B.601/55 C. 11/120 D.120/11.

FIND ODD MAN OUT

1. 3, 5, 11, 14, 17, 21

A. 21 B. 17 C. 14 D. 3

2. 8, 27, 64, 100, 125, 216, 343

A. 27 B. 100 C. 125 D. 343

3. 10, 25, 45, 54, 60, 75, 80

A. 10 B. 45 C. 54 D. 75

4. 396, 462, 572, 396, 427, 671, 264

A. 396 B. 427 C. 671 D. 264

5. 6, 9, 15, 21, 24, 28, 30

A. 28 B. 21 C. 24 D. 30.

6. 1, 4, 9, 16, 23, 25, 36

A. 9 B. 23 C. 25 D. 36

7. 1, 4, 9, 16, 20, 36, 49

A. 1 B. 9 C. 20 D. 49

8. 2, 5, 10, 17, 26, 37, 50, 64

A. 50 B. 26 C. 37 D. 64

9. 10, 14, 16, 18, 21, 24, 26

A. 26 B. 24 C. 21 D. 18

10. 16, 25, 36, 72, 144, 196, 225

A. 36 B. 72 C. 196 D. 225

11. 331, 482, 551, 263, 383, 362, 284

A. 263 B. 383 C. 331 D. 551

12. 835, 734, 642, 751, 853, 981, 532

A. 751 B. 853 C. 981 D. 532

13. 41, 43, 47, 53, 61, 71, 73, 81

A. 61 B. 71 C. 73 D. 81

14. 3, 5, 7, 12, 17, 19

A. 19 B. 17 C. 5 D. 12