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AVERAGE SPEED, RELATIVE SPEED, BOATS AND STREAMS-1 1. A boat moves a certain distance upstream in 10hours,while it takes 2 hours to move the same distance downstream. If the speed of the boat is 30km/hr , the time taken for a log to float 40km downstream. a)2 hrsb)3hrsc)4hrs d)5hrs2.A car travels from point P to point Q in 10hrs. It then travels a distance Q to R in 15 hrs. If PQ is half of the distance between Q and R, find the ratio of the times that would be taken by the car to travel the distance PR if it travelled PR with the average speed it took to travel QR to that it would take to travel PR with the average speed it took to travel PQ a)1/2 b)2/5 c)3/4 d)5/63. A faster boat with speed 20km/hr is chasing a slower boat with speed 15km/hr, If the initial distance of separation of the boats were 25km, and both boats were moving downstream ,then when would the faster boat catch up with the slower one, given that the speed of the stream is 5km/hr? a)3hrs b)5hrs c)6hrs d)7hrs4. A faster boat with speed 20 km/hr is chasing a slower boat with speed 15km per hour, if the initial distance of separation of the boats were 25km,and both boats were moving downstream, Calculate the difference between the distances that the faster boat would have to travel in each case to catch up with the slower boat? a)25km b)20km c)30km d) cannot be determined5. A man travelled 1/4th of a certain distance by bus, 1/3rd of the distance by car and rest of the distance he walked. Calculate the average speed of the man if the ratio of the times taken to travel the distance were 3:2:7 respectively. The walking speed of the man is 5km/hr

a) 7kms/hr b) 8kms/hr c)9kms/hr d)none

6.A car theft occurs and the felon drives away at a constant speed of 70km/hr. By the time the theft is reported the accused is already 50km away from the nearest police station and the police jeep begins chasing the car at a constant speed of 80km/hr. When the gap between the stolen vehicle and the police jeep reduces to 30km, the thief increases his speed at a constant rate per hour and thereby just manages to escape conviction. Find the rate at which the thief increases his speed. a) 10kms/hr b) 1 km/hr c) 10/9 kms/hr d) 10/7 km/hr

7. In the above problem i.e problem (6), if the police jeep constantly increased it speed by 20km/hr for every hour starting fro the end of the 1st hour of its chase and the thief increased his speed by 10km/hr for every hour starting from the end of the 1st hour of chase,in what time does the police keep catch up with the stolen car? A)4 hrs b)5hrs c)3hrs d)2hrs8. A boat travels a certain distance upstream in 10hrs and it returns the same distance downstream in 5hours, what would be the time taken by the boat to travel the same distance up and down in still water? A) 10hrs b)15hrs c) 12hrs 30mins d) 13hrs 30mins9.A certain distance was supposed to be covered by the driver of a car in a certain time t, but after travelling half the distance with the required speed, the driver was forced to reduce his speed by 50% for half the remaining distance owing to poor visibility. If the driver double his original speed for the remaining part of his journey, find the fraction of time by which he was late a)1/4 b)1/8 c)1/6 d)1/7

10. A train starts from Kolkata towards midnapore at 4pm. At the same time another train leaves midnapore for Kolkata. By the time they meet , it is seen that the train from Kolkata has travelled 50km more than the train from midnapore.If the Distance between midnapore and Kolkata is 150km, then how far from Kolkata will the train from midnapore be when the train from Kolkata just reaches midnapore assuming that both trains maintain the same respective constant speed.a)75 b)50 c)100 d)none

AVERAGE SPEED, RELATIVE SPEED , BOATS AND STREAMS-2

1. A car leaves Kolkata at 6am for midnapore. At 10am it meets a biker who started from midnapore at 5am the same day.At 2 pm the car reaches midnapore. When does the biker reach Kolkata?( Assume that all vehicles maintain constant speeds) a)2pm s c)4pm d) 5pm

2.two trains running along parallel tracks on opposite directions take 20seconds to cross each other. However if they were running in the same direction, the longer train would take 40seconds to cross the shorter train. If the length of the longer train is halved, the time taken by the trains to cross each other decreases by 16 seconds.What would be the time taken by the longer train to cross a bridge thrice its own length , given that the slower train is 75% the length of the faster train? A) 320/7secs b)480/7secs c)500/7secs d)cannot be determined

3. A boat X sets sails downstream from the point A towards the point B. It crossed the point B and proceeds towards a point C downstream . just as the boat crosses the point B, another boat Y sets off from the point A towards B. The boat X reaches C and turns back only to meet Y at D, the midpoint of AC. AB is 1/3rd of AC and the speed of the stream is 1/3rd the speed of boat X is still water and both boats maintain their same respective engine performances throughout the journey. Find the ratio of the speeds of boat X and boat Y in still water.

a) 17:8 b)13:1 c)21:1 d)5:2 4. Cars A,B,and C set out from X at 4am, 5am, and 6am respectively towards a point Y which is their destination , and they move with their respective constant speeds. Car C overtakes car A at 10am and car B at 9am and reaches Y at 12am. When does car B overtake car C?

a) 1pm b)2pm c)3pm d)none5. In the above question (4) find the ratio of the spees of cars A,Band C

a)8:9:12 b)7:3:9 c)5:4:9 d)none

6. A train crosses a railway bridge in 100 seconds and a lamp post in 10 seconds. Another train crosses the very same railway bridge in 200 seconds and a lamp post in 20 seconds.Find the time taken by one of the trains to overtake the other. a)80secs b)40secs c)70secs d)cannot be determined7.one morning I woke up late and hence missed the bus that takes me to office. I instructed my driver to follow the same route that the bus takes which incidentally is a straight road so that I might catch up with the bus. The driver took exactly 15mins to catch up with the bus and I reached office 1 hour later. That day the driver who always maintains a constant speed when he drives, picked me up from office at 5pm and we reached home by 5.45pm. How long does the bus take me to reach office?a)2hrs b)1.1/2 hrs c)3hrs d)cannot be determined

8. My office usually ends at 6pm when my driver picks me up and drives off for home. One day my driver called me on my mobile that the car was giving some engine trouble and so he had to halt for repair work I started walking towards home at 6pm and walked for thirty minutes when I met my driver coming from the opposite direction.If the ratio of the speed of the car to my walking speed is 5:1, then how long did the repair work take place? A)24mins b)30mins c)6mins d)cannot be determined9.In addition to the data given in the above problem , suppose it is known that I usually reach home at 7.30pm,then on that day when the car suffered engine trouble,when did I reach home?

a)8pm b)7.42pm c)7.48pm d)9pm10. The time taken for two boats A and B separated by a certain distance d and moving in opposite directions in still water is 10seconds. The speed of boat A is twice that of the speed of boat B.If the separation between the boats be 2d and both boats move upstream in a river with boat A chasing boat B and the speed of the stream being one third of that of the slower boat,how long does boat A takes to catch up with boat B. a) 20secs b)30secs c)60secs d)cannot be determined

TSD RACES,CIRCULAR TRACKS, CLOCKS 21.romeo and Juliet start simultaneously from the same point and run in opposite direction in a circular track of length 6400m with speeds 15m/sec. However each time they meet they double their respective speeds.how much time elapsed since the start when they meet for the 5th time since start?

a)620secs b)580secs c)400secs d)720secs

2.In the above problem (1),what was the distance covered by romeo till they met for the fourth after start? A)19200m b)24600m c)12800m d)15600m

3.In a race of n participants, numbered 1,2,3n around a circular track, n being greater than 1, all runners start from the same point.The speeds of the runners are x,2x,3xnx respectively.Assuming that there are 10 runners and they run in the same direction,how many distinct meeting points on the circular track exist where two or more runners meet a)27 b)29 c)28 d)304. In a race of n participants, numbered 1,2,3n around a circular track, n being greater than 1, all runners start from the same point.The speeds of the runners are x,2x,3xnx respectively. Assuming there are three runners , namely 1,2and 3 and 1and 2 run in opposite directions and 3 runs in the same direction as runner 1,how many distinct meeting points are possible where two or more runners meet?a)8 b)7 c)9 d)10

5.Two runners A and B starting from points Xand Y respectively and simultaneously move towards each other and meet after 10mins after which A continues towards Y and B continues towards X upon reaching Y and X respectively.A and B continue on their return journeys and they continue to move to and fro meeting each other 7 times in succession,each time both of them moving in opposite directions.How long after the start, do the runners meet for the seventh time?

a)70mins b)100mins c)130mins d)cannot be determined

6.Two cars A and B set out simultaneously from the points X and Y towards Y and X respectively with their constant speeds. They meet at a point K which is 50km from Y after which car A sets off towards Y and turns back and overtakes car B(B has not yet reached X) at a point 60km from X.find the distance between Xand Y. a)105+10 sqrt(201)km b)105-10 sqrt(201)km b)105+10 sqrt(167)km d)none7.Three runners A,B,C have stride lengths 3:4:7.However the ratio of the numbers of strides taken by them in a fixed period of time is 6:3:4 respectively. In a race of 6300m, what should be the head start given by the fastest runner to the two other slower runners so that all of them finish the race the same time. A)4050m,3600m b)2250m,3600m c)4050m,2700m d)cannot be determined

8.Two cars A and B are moving towards each starts simultaneously from Xand Y maintaining constant Speeds.They meet at a point K after which they set off for their respective destinations.Upon reaching their destinations they turn and A starts moving towards X and B moves towards Y and meet at a point L,L being closer to X than K.If LK is 50km and the speed ratio of the cars Aand B is 4:3,find the distance between Xand Y a)150.67km b)106.52km c)117.32km d)cannot be determined

9.At what time between 4pm and 5pm will the hands of a clock be coincides with each other?

a)21 9/11mins past 4pm b)4.15pm c)23 1/11 mins past 4pm d)none10.Find the angle between the hour hand and the minute hand of a clock at 4.30pm.

a) 200 b)400 c)450 d)500

RATIO PROPORTION AND VARIATION1.find out the ratio whose value is 2/3 and the antecedent is 18.

A)18:27 b)2:3 c)20:30 d)180:20 e)27:182. 2/3 : 5/6 :: 8/7: ? a)17/14 b)10/7 c)5/3 d)13/14 e)9/6

3. A:B = 2:3, B:C= 4:5, C:D=6:7 find the ratio of A and D

a) 4:13 b)8:35 c)7:24 d)8:22 e)16:354.two equal glasses are respectively 1/3 and full of milk. They are then filled up with water and the contents are mixed in a tumbler.Find the ratio of milk and water in the tumbler.

a) 1:5 b)7:17 c)3:9 d)2:5 d)3:75. If in 30 litres of a mixture of milk and water the ratio of milk and water is 7:3 ,find out the quantity of water to mix in order to make this ratio 3:7 a)40 b)10 c)30 d)20 e)496.In a bag there are coins of 25paise ,10paise and 5paise in the ratio 1:2:3.If there are in all Rs.30, how many 5paise coins are there? A)50 b)100 c)150 d)200 e)120

7.Shyam has a sister who is half the age of his age.When Shyams age doubles, what will be the ratio of his age to his sisters age? a)6/5 b)4/3 c)5/2 d)3/2 e)3/4

8.On a certain day railway the 1st and 2nd class fares are 7paise and 3 paise per km .Aman who travelled 100km spent rs.340 in going part of distance by first class and the remaining in second class. How many km did he travel in 1st class? A)30 b)48.5 c)90 d)51.5 d)979.ratio of As age to Bs age is equal to 4:3 .A will be 26 years old after 6years , how old is B now?

a)10 1/2yrs b)21yrs c)12yrs d)15yrs e)5yrs

10. 25men with 10 boys can do as much work in 6days as 21men with 30boys can do in 5days.How many boys must help 40men to do the same work in 4 days?

a)5boys b)40boys c)20boys d)10boys e)12boys

RATIO AND PROPORTION 21.A contractor took a contract for building 12 km road in 15days and employed 100labours on the work. After 9days he found that only 5km road had been constructed .how many more labours should be employed to ensure that the work may be completed within the given time?

a)120 b)90 c)110 d)100 e)none

2.what number has 5 to I ratio to the number 10? A)42 b)55 c)50 d)62 e)none

3.15men do a work in 20days.In how many days will 20men do the full work?

a)30days b)15days c)40days d)20days e)none

4. three persons start business and make profit of Rs.1180. If their capitals are as 1/5 : 1/6 : 1/8, how should the profit be divided? A)500,380,300 b)490,390,300 c)480,400,300 d)470,420,490 e)none5. A,B and C purchased the mangoes in a ratio 5:3:2 . If the difference of mangoes of A and C is 60. Find out the total number of mangoes purchased by them. A)200 b)150 c)250 d)300 e)none

6.Acompany makes profit of Rs 450.out of this 20% is paid for taxes and the rest be divided among its partners A,B and C in proportion of 1: :2 . Find the share of each

a)120,80,160 b)160,80,120 c)80,120,160 d)120,160,80 e)none

7.A garrison of 2200men has provision for 16weeks at the rate of 45gm per day per men.How many men must leave so that the same provision may last for 24weeks at 33gm per day per men?

a)200 b)1125 c)2000 d)250 e)none

8. If 5 men can do a piece of work in 20days ,in how many days will 10men and 5 boys do the same work if 1 man does as much work as 2 boys? a)8 b)10 c)12 d)36 d)none

9. If 21 cows eat as much as 15 oxen,how many cows will eat as much as 25 oxen?

A)30 b)35 c)25 d)36 e)none

10.there are three containers of equal capacity .first container is half full, second is one third full and third is empty.If all the water in the containers is divided equally among the containers,what part of the container will be full? A)1/3 b)2/9 c)5/18 d)1/6 e)none

PERCENTAGE PROFIT AND LOSS PARTNERSHIP 11.A base ball team has lost 7 games and has won 13 games. What percent of the games played did they win? A)35 b)65 c)50 d)30 e)70

2. 60% of 35 is what percent of 400? A) 1 b)2 c)3 d)6 e)5

3. If 1 out of every 50 people who play a certain games win a prize, what percent of people lose?

a) 1% b)2% c)99% d)98% e)49%4. The air consists of 79.2% of nitrogen, 20.7% of oxygen, 0.08% of other light gases and the remaining gas is argon. find out the volume of the air consisting one cubic meter of Argon

a)500 Cu.meter b)50 Cu.meter c)5 Cu.meter d)5000Cu.meter e)50,000Cu.meter5.In an examination 49.3% of total students appeared, passed successfully.If the number of successfully candidates are 23128 how many students appeared in the exam?a)46903 b)45913 c)47913 d)46000 e)469136.A tank is filled in 10% in one hour and 8% of the water is emptied in the next hour. If it is repeated again, find the percentage of tank filled with water. A)20% b)4% c)19% d)17.66% e)19.2%

7.If 20% of mans salary is paid as rent, 60% are his living expenses and 10% is paid in L.I.C. If he spends remaining Rs.30 on the education of the children,find his salary.

a) Rs.300 b)Rs.100/3 c)Rs.3000 d)Rs.900 e)none of these

8.A litre of water is evaporated from 6 litre of sugar solution containing 4% of sugar. Find the percentage of sugar in remaining solution. A)3 1/3 b)4 4/5 c)4 d)5 e)3

9.When the price of cloth was reduced by 25% the quantity of cloth sold is increased by 20%. What was the effect on gross receipt of the shop? a)5% increase b)5% decrease c)no change d)10%increase e)none10. Chinmony sold his ratio set at 10%loss.If he would have sold it for Rs.45 more, he would have made 5% profit. For how much did he sell the radio? A)Rs.315 b)Rs270 c)Rs300 d)Rs345 e)Rs350

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