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Crack The Iim Indore Ipm Entrance Examination 2nd Edition North Academics (Author) - Solutions

If the 9 times the 9th term in AP is equal to 15 times the 15th term in the AP, then what is the 24th term?(a) –1 (b) –3(c) 0 (d) 1
The 5th term of an AP is 15 and the 9th term is 23.Find out the 14th term.(a) 31 (b) 33(c) 35 (d) 37
The product of n positive numbers is 1.Their sum is(a) a positive integer.(b) divisible by n.(c) equal to n n+1 .(d) greater than or equal to n.
The 288th term of the seriesa, b,b, c,c, c,d,d, d,d, e,e, e,e, e, ... is(a) u (b) v(c) w (d) x
The ratio of HM and GM for two positive numbers is 4:5. What is the ratio of the numbers?(a) 4:1 (b) 3:2(c) 3:4 (d) 2:3
Find out the first term of the infinite GP whose first two terms add up to 5, and whose each term is three times in the sum of all terms that follow it.(a) 1 (b) 2(c) 3 (d) 4
Sum of three numbers in GP is 70.If the two extreme terms are multiplied by 4, and the middle term by 5, the resultants are in AP. Find out the numbers?(a) 10, 25, 35 (b) 10, 20, 40(c) 15, 30, 35 (d) 12, 24, 34
If the sum of an AP is the same for p terms as for q terms, then find out the sum for (p + q)terms?(a) 2 (b) 0(c) 4 (d) None of these
Find outa, b, c between 2 and 18 such that(i) their sum is 25, (ii) 2,a, b are consecutive terms of an AP, and (iii)b, c, 18 are the consecutive terms of a GP?(a) 5, 8, 14 (b) 4, 8, 12(c) 5, 8, 12 (d) None of these.
An AP has 23 terms. The sum of the middle three terms is 144.The sum of the last three terms is 264.What is the 16th term?(a) 102 (b) 64(c) 82 (d) None of these.
A man arranges to pay off a debt of ` 3,600 by 40 annual installments which form an AP. When 30 of the installments repaid, he dies leaving 1/3rd of the debt unpaid. What was the value of the first installment?(a) 50 (b) 51(c) 52 (d) 53
Find out the first term?(a) 4 (b) 5(c) 3 (d) None of these.
The sum of 15 terms of an AP is 600, and the common difference is
In a GP, the first term is 7 and the nth term is 448.The sum of n terms is 889.What is the common ratio of this GP?(a) 2 (b) 4(c) 1 (d) 3
Find out the sum of all the numbers divisible by 6 in between 100 and 400.(a) 12,550 (b) 12,450(c) 11,450 (d) 11,550
Find out the sum of the first 15 terms of the series whose nth term is (4n + 1).(a) 485 (b) 495(c) 505 (d) 630
Two guns were fired from the same place at an interval of 10 minutes and 30 seconds, but a person in the train approaching the place hears the second shot 10 minutes after the first. The speed of the train (in km/h), supposing that speed travels at 330 metres per second, is:(a) 19.8 (b) 57.6(c)
At his normal speed, Rishu can go 18 km downstream in a flowing river in 9 hours less than what he takes to go the same distance upstream. The downstream journey would take 1 hour less than what the upstream journey would take provided he doubles his rate of rowing. Find the speed of the river (in
X, Y and Z walk at 6, 12 and 18 km/h respectively. They start from Jhumritalaiya towards Delhi at 2, 5 and 7 pm respectively, when Y catches up with X, Y sends X back with a message to Z; when will Z get the message?(a) 9:45 pm (b) 9 pm(c) 8:45 pm (d) 9:15 pm
A runs 1.75 times as fast as B. If A gives B a start of 60 m, how far must be the winning post be so A and B reach it at the same time?(a) 140 m (b) 70 m(c) 210 m (d) 175 m
A and B start at the same time from P and Q (55 km apart) to Q and P at 3 and 2½ km/h respectively. They meet at R, reach Q and P, return immediately and meet again at S. The distance from R to S is:(a) 10 km (b) 12 km(c) 15 km (d) 16 km
A can give a lead 20 m to B in a race of 200 m and B can give a lead of 10 m to C in a race of 200 m. By how many metres can A beat C in the same race of 200 m?(a) 21 m (b) 28 m(c) 29 m (d) 31 m
A man can swim with the stream at the rate of 3 km/h and against the stream at the rate of 2 km/h. How long will it take him to swim 7 km in still water?(a) 3 hours (b) 2.8 hours(c) 2.6 hours (d) 3.2 hours
Anand can beat Bidhan by 5 metres in a 100 m race and Bidhan can beat Chandan by 10 metres in a 200 m race. Then in a race of 400 m, Anand can beat Chandan by:(a) 40 metres (b) 39 metres(c) 15 metres (d) 10 metres
Two trains start at the same time from A and B and proceed towards B and A at 36 km/h and 42 km/h respectively. When they meet, it is found that one train has moved 48 km more than the other. Then the distance between A & B (in km) is:(a) 624 (b) 636 (c) 544 (d) 460
For covering a distance P km, a man takes t hour. If he moves 3 km/h faster, he takes 40 minutes less. But if he moves 2 km/h slower, he takes 40 minutes more. Then P is equal to:(a) 22.5 km (b) 32.5 km(c) 42.5 km (d) None of these.
Excluding stoppages, the speed of a bus is 54 km/h and including stoppages it is 45 km/h. What is the stoppages time of bus(in minutes) per hour?(a) 10 (b) 12(c) 9 (d) 20
A man rows a boat upstream a certain distance and then returns to the same place.If the time taken by him in going upstream is twice the time taken in rowing downstream, find the ratio of the speed of the boat in still water and the speed of stream.(a) 2:1 (b) 3:2(c) 5:3 (d) 3:1
A ship 156 km away from the sea coast springs a leak, which admits 2.33 metric tons of water in 6.5 minutes, but the pumps throw out 15 metric tons of water in 1 hour.70 metric tons would suffice to sink the ship. What is the average speed (in km/h)so that the ship may just reach the shore as ship
Amit Kumar starts driving from Patna to Quillon at 9 am and Bhartendu starts driving from Quillon to Patna at 10 am.Bhartendu is 50% faster than Amit Kumar.What is the time when they meet if Patna and Quillon are 300 km apart and Amit Kumar’s speed is 50 km/h?(a) 12.30 pm (b) 12 noon(c) 11 am (d)
At noon, ship Vikrant starts from a point P towards a point Q and at 1.00 pm, ship Viraat starts from Q towards P. If ship Vikrant is expected to complete the voyage in 6 hours and ship Viraat is moving at a speed 2/3 of that of ship Vikrant, at what time are the two ships expected to meet?(a) 4 pm
Shramjeevi Express leaves Patna for New Delhi at 10:10 am and reaches New Delhi at 3:30 pm. Magadh Express leaves New Delhi at 9:48 am and reaches Patna at 2:36 pm.If routes of both the trains are same, then at what time both the trains will meet each other?(a) 12:52 pm (b) 1:12 pm(c) 1:32 pm (d)
What is the speed of a train, which overtakes a cow walking at a speed of 5 km/h in 30 seconds, if the train is 274 metres long?(a) 51.88 km/h (b) 27.88 km/h(c) 37.88 km/h (d) 21.67 km/h
In a race of 300 m, Abhishek beats Bijay by 30 metres while Bijay beats Chandan by 50 metres. By what distance must Abhishek have beaten Chandan in the same 300 m race?(a) 80 metres (b) 40 metres(c) 160 metres (d) 75 metres
Two persons, 27 km apart, setting out at the same time are together in 9 hours if they walk in the same direction, but in 3 hours if they walk in opposite directions. What are their speeds (in km/h)?(a) 5, 4 (b) 4, 3(c) 6, 3 (d) 8, 7
A train travels from a station P to another station Q, a distance of 192 km at an average speed of 80 km per hour. It then travels back to P and the total time taken by it for the return journey is 5 hours 36 minutes. Find the average speed of the train on the return trip to P.(a) 72 km/h (b) 36
Shilu can go 30 km upstream and 44 km downstream in 10 hours. Also, she can go 40 km upstream and 55 km downstream in 13 hours. What is her speed in still water?(a) 6 km/h (b) 12 km/h (c) 8 km/h (d) 16 km/h
Sama traveled half the distance from her house to school at a speed of 10 km/h and for exactly half of the remaining time she traveled at 15 km/h and the rest of the time at 20 km/h. Find her average speed.(a) 13 km/h (b) 128/11 km/h(c) 15 km/h (d) None of these.
Sona travels 600 km to his home partly by train and partly by car. She takes 8 hours if she travels 120 km by train and the rest by car. She takes 20 minutes more if she travels 200 km by train and the rest by car.Find the speed of the train in km/h.(a) 45 (b) 60(c) 75 (d) None of these.
Shramjeevi Express goes to Patna from New Delhi at a speed of 60 km/h. At what speed(in km/h) should Shramjeevi Express return from Patna to New Delhi so that average speed during the whole journey is 120 km/h?(a) 180(b) 240(c) 120(d) This is not possible
Difference between time taken in covering a certain journey decreases by 45 minutes when speed is increased to 20 km/h from 10 km/h. What is the difference between the time taken when the same distance is covered at a speed of 40 km/h and 25 km/h?(a) 12.5 mins (b) 13.5 mins(c) 18 mins (d) None of
When speed of a train is increased by 20%, it takes 20 minutes less to cover the same distance. What is the time taken to cover the same distance with the actual speed?(a) 2 hours (b) 1 hour(c) 1.5 hour (d) 2.5 hour
A train M leaves Meerut at 5 am and reaches Delhi at 9 am. Another train leaves Delhi at 7 am and reaches Meerut at 10.30 am. At what time do the two trains cross each other?(a) 7.36 am (b) 7.56 am(c) 8 am (d) 8.26 am
A car covers a distance of 715 km at a constant speed. If the speed of the car would have been 10 km/h more, then it would have taken 2 hours less to cover the same distance. What is the original speed of the car?(a) 45 km/h (b) 50 km/h(c) 55 km/h (d) 65 km/h
Walking 6/7th of his usual speed, a man is 12 minutes too late. The usual time taken by him to cover that distance is:(a) 1 hour (b) 1 h 12 min(c) 1 h 15 min (d) 1 h 20 min
The average speed of a train in the onward journey is 25% more than that in the return journey. The train halts for one hour on reaching the destination. The total time taken for the complete to and fro journey is 17 hours, covering a distance of 800 km.The speed of the train in the onward journey
A car driver travels from the plains to the hill station, which is 200 km apart at an average speed of 40 km/h. In the return trip, he covers the same distance at an average speed of 20 km/h. The average speed of the car over the entire distance of 400 km is:(a) 25 km/h(b) 26.67 km/h(c) 28.56
Two trains are running on parallel lines in the same direction at the speed of 50 km/h and 30 km/h respectively. Given that the faster train crosses a man in the slower train in 18 seconds, what is the length of the faster train?(a) 170 m (b) 100 m (c) 98 m (d) 85 m
On a river, Q is the mid-point between two points P and R on the same bank of the river. A boat can go from P to Q and back in 12 hours, from P to R in 16 hours 40 minutes. How long would it take to go from R to P?(a) 3.33 hours (b) 5 hours(c) 6.66 hours (d) None of these.
In a km race, Amit beats Bahadur by 100 m and Bahadur beats Chandra by 200 m. By how many metres does Amit beat Chandra in the same race?(a) 100 m (b) 83⅓ m(c) 68 m (d) 280 m
A man can row 1/2 km against the current in 12 minutes and returns in 6 minutes. Find the speed of the current.(a) 1.25 km/h (b) 1.5 km/h(c) 2.5 km/h (d) 3 km/h
Two trains started from a station, at the same time in the same direction, at speeds of 70 km/h and 60 km/h. What will be the distance between the two trains after 6 hours?(a) 42 km (b) 54 km(c) 60 km (d) 84 km
A train, 225 m long, is running at 45 km/h.In what time does it cross a man running at 18 km/h in the same direction?(a) 20 seconds (b) 30 seconds(c) 25 seconds (d) 15 seconds
In a kilometer race, A beats B by 10 metres.In a 2 kilometres race, A beats B by:(a) 10 m (b) 20 m(c) 40 m (d) 25 m
A car travels from Patna to Jehanabad at the speed of 65 km/h in one hour. If the speed is reduced by 15 km/h then, how much more time will the car take to cover the same distance?(a) 12 minutes (b) 16 minutes(c) 18 minutes (d) 44 minutes
Anil calculated that it will take 45 minutes to cover a distance of 60 km by his car. How long will it take to cover the same distance if the speed of his car is reduced by 15 km/h?(a) 36 minutes (b) 60 minutes(c) 48 minutes (d) None of these.
A person can row a distance of 1 km upstream in 10 minutes and downstream in 4 minutes. What is the speed of the stream?(a) 4 km/h (b) 9 km/h(c) 5.6 km/h (d) 4.5 km/h
A certain distance is covered at a speed V km/h. If half of the same distance is covered in double the time, then the ratio for the former speed to that of the latter is:(a) 4:1 (b) 1:4(c) 2:1 (d) 1:2
Speed of a train is 88 km/h. What time will it take to cross a platform 180 m long if the length of the train is 150 m?(a) 11½ seconds (b) 10½ seconds(c) 13½ seconds (d) 14½ seconds
A train having a length of 400 m, travelling at a speed of 15 m/s, crosses a platform in one minute. What is the length of the platform?(a) 2,000 m(b) 500 m(c) 400 m(d) Cannot be determined.
The speed of a train is 20 m/s. The time it takes to cross a telephone pole is 10 seconds.What is its length?(a) 100 m (b) 1.5 km(c) 150 m (d) 200 m
A man is running at the speed of 36 km/h, then how many metres does he cover in 40 seconds?(a) 400 m (b) 300 m(c) 2,400 m (d) 100 m
The monthly income of A and B are in the ratio of 3:2, and their expenditures are in the ratio of 5:3. If each of them saves` 1,000 a month, then what is the income of A?(a) ` 4,000 (b) ` 6,000(c) ` 9,000 (d) None of these
The value of a diamond varies directly as the square of its weight. If a diamond worth` 10,000 is divided into 2 pieces in the ratio of 4:6, what is the loss in value?(a) 52% (b) 48%(c) 36% (d) None of these.
If A:B = 3:4. What will be the value of(3A2 + 4B)/(3A – 4B2)?(a) 43:55(b) –43:55(c) Either (a) or (b)(d) Cannot be determined.
Satish used 6 L of oil paint to paint a map of India of 6 m high. How many litres of paint would Santosh need for painting a proportionally scaled map of height 18 m?(a) 54(b) 18(c) 30(d) Cannot be determined.
If the number of guavas is 21, then which of the following can be the total number of all the in the basket?(a) 63 (b) 89(c) 101 (d) 117
If total number of fruits is 61, then find the number of guavas.(a) 16(b) 20(c) 25(d) Cannot be determined.
Two alloys of chromium have different percentage of chromium in them. First one weighs 6 kg and second one weighs 12 kg.One piece each of equal weight was cut off from both the alloys and the first piece was alloyed with the second alloy and the second piece alloyed with the first one. As a result,
A watermelon is cut into two pieces in the ratio 3:5 by weight. The bigger of the two is cut further in the ratio 5:7 by weight.Find the ratio of each of the three pieces.(a) 3:5:7 (b) 36:25:35(c) 15:25:56 (d) None of these.
P works twice as fast as Q, whereas P and Q together can work three times as fast as R. If P, Q and R together work on a job, in what ratio should they share the earnings?(a) 2:1:1 (b) 4:2:1(c) 4:3:2 (d) 4:2:3
Ratio of age of Sita and her mother is 2:3.N years from now, ratio of their ages will become 3:5. What is the value of N?(a) Infinite(b) 1(c) More than 1 but finite(d) Not possible
A rat takes 5 leaps for every 4 leaps of a cat, but 3 leaps of the cat are equal to 4 leaps of the rat. What is the ratio of the speed of the rat to that of the cat?(a) 11:15 (b) 15:11(c) 16:15 (d) 15:16
What is the total number of chapters in the book?(a) 113 (b) 226(c) 127 (d) None of these.
What is the total number of pages in the book?(a) 4,000 (b) 4,800(c) 4,200 (d) 4,600
A metal trader buys 2 kinds of silver foils, the ratio of their prices being 1:4. He sells the alloy at ` 90 per kg so that he can make a profit of 20%. If ratio of their quantities present in a alloy is 6:1 respectively, find the purchase price of foil present in lesser quantity.(a) ` 52.5 (b) `
Two software developers Vinit and Harpal share a mainframe and the final cost is` 74,750. Vinit uses 5 type I terminals for 7 weeks and 22 type II terminals for 4 weeks. Harpal uses 10 type I terminals for 6 weeks and 8 type II terminals for 6 weeks. If cost of operating each type I and type II
Gandhiji owned cows, some black and some white. He found that 4 black cows and 3 white cows give the same amount of milk in 5 days as 3 black cows and 5 white cows give in 4 days. What is the ratio of milk given by a black cow in a day to that given by a white cow in a day?(a) 8:5 (b) 5:8(c) 3:5
Population of the Balearic Island situated in Mediterranean Sea is 18,000. Balearic Island has three ports A, B and C. Every year the entire population of each port moves to the other two ports, half going to one of them and the remaining half going to the other. The current populations of A, B and
Sum of four numbers is 253.The ratio of the first number to the second number is 2:3. The ratio of the second number to the third number is 5:6. The ratio of the third number to the fourth number is 8:9. What is the average of the second number and the third number?(a) 72 (b) 132(c) 60 (d) None of
Ratio of income of A and B is 5:4 and the ratio of their expenditure is 3:2. At the end of the year, each saves ` 1,600. What is the income of A?(a) ` 3,400 (b) ` 3,600(c) ` 4,000 (d) ` 4,400
Three jars have their volumes in the ratio 3:4:5. They are full of mixtures of milk and water. The mixtures contain milk and water in the ratio of (4:1), (3:1) and (5:2)respectively. The contents of all these three jars are poured into a fourth jar.The ratio of milk and water in the fourth jar
85 litres of a solution contains milk and water in the ratio 27:7. How much more water is to be added to get a new solution containing milk and water in the ratio 3:1?(a) 5 litres (b) 6.5 litres(c) 7.25 litres (d) 8 litres
Number of students for Mathematics, Physics and Biology in a school are in the ratio 5:7:8.If number of these seats is increased by 40%, 50% and 75% respectively, what will be the ratio of students after the increase?(a) 2:3:4 (b) 6:7:8(c) 6:8:9 (d) None of these.
60 kg of an alloy A is mixed with 100 kg of alloy B. If alloy A has lead and iron in the ratio 3:2 and alloy B has iron and copper in the ratio 1:4, then the amount of iron in the new alloy is:(a) 36 kg (b) 44 kg(c) 53 kg (d) 80 kg
The ratio of the number of boys and girls in a school is 3:2. If 20% of the boys and 25% of the girls are scholarship holders, what percentage of the students does not get the scholarship?(a) 56 (b) 70(c) 78 (d) 80
A sum of ` 53 is divided among A, B, C in such a way that A gets ` 7 more than what B gets and B gets ` 8 more than what C gets. The ratio of their shares is:(a) 16:9:18 (b) 25:18:10(c) 18:25:10 (d) 15:8:30
Ratio of the earnings of A and B is 4:7.If the earnings of A increase by 50% and those of B decrease by 25%, the new ratio of their earnings becomes 8:7. What are A’s earnings?(a) ` 21,000 (b) ` 26,000 (c) ` 28,000 (d) Data inadequate
A sum of money is to be distributed among Amar, Bidya, Charu and Dhanraj in the proportion of 5:2:4:3. If Charu gets ` 1,000 more than Dhanraj, what is Bidya’s share?(a) ` 500 (b) ` 1,500(c) ` 2,000 (d) None of these.
` 366 are divided amongst A, B and C so that A may get 1/2 as much as B and C together, B may get 2/3 as much as A and C together, then the share of A is:(a) ` 122 (b) ` 129.60(c) ` 146.60 (d) ` 183
` 1,210 is divided among A, B, C so that A:B = 5:4 and B:C = 9:10. Then, C gets:(a) 340 (b) 400(c) 450 (d) 475
Two numbers are in the ratio 3:5. If 9 is subtracted from each, the new numbers are in the ratio 12:23. The smaller number is:(a) 27 (b) 33(c) 49 (d) 55
If ` 782 be divided into three parts, proportional to 1/2:2/3:3/4, then the first part is:(a) ` 182 (b) ` 190(c) ` 196 (d) ` 204
If (a + b):(b + c):(c +a) = 6:7:8 and(a + b +c) = 14, then the value of c is:(a) 6 (b) 7(c) 8 (d) 14
If (x:y) = 2:1. Then (x2 – y2):(x2 + y2) is:(a) 3:5 (b) 5:3(c) 1:3 (d) 3:1
If x:y = 5:2, then (8x + 9y): (8x + 2y) is:(a) 22:29 (b) 26:61(c) 29:22 (d) 61:26
If 2A = 3B and 4B = 5C, then A:C is:(a) 4:3 (b) 8:15(c) 15:8 (d) 3:4
If 2A = 3B = 4C, then A:B:C is:(a) 2:3:4 (b) 4:3:2(c) 6:4:3 (d) 20:15:2
If A:B = 8:15, B:C = 5:8 and C:D = 4:5, then A:D is equal to:(a) 2:7 (b) 4:15 (c) 8:15 (d) 15:4
If A:B = 5:7 and B:C = 6:11, then A:B:C is:(a) 55:77:66 (b) 30:42:77(c) 35:49:42 (d) None of these.

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