Arithmetic session Q1. The average marks of the girls in a class is equal to the number of boys and the average marks of boys is equal to the number of girls. If the class average is 4 less than the average of the boys' average marks and the girls' average marks, which of the following could be the number of students in the class? 1.24 2.48 3.50 4.64 Q2. There are three vessels A, B and C having mixtures of milk and water. Concentration of milk in the vessels is C1, C2 and C3 respectively. When a part of vessel A is replaced with the mixture in vessel B, then the concentration of milk in the final mixture is less than C1. However, when vessels B and C are mixed in the ratio 1:1, then the concentration of milk in the final mixture is double than the concentration of milk in the vessel B. Which of the vessels is having the mixture of maximum concentration of milk? 1. A 2. B 3. C 4. cannot be determined Q3. Ten different samples of milk solution – A, B, C, D, E, F, G, H, I and J are taken and the concentration of each sample (total quantity of milk as a percentage of total quantity of solution) was found out and the results were tabulated as follows: Sample Concentration (%) A 78 B 57 C 82 D 84 E 98 F 66 G 34 H 87 I 79 J 71 If two samples are taken and it is required to form a sample whose concentration is more than 80%, then a maximum of how many distinct pairs of samples are there, which will never give the desired result for any ratio of the volume? 1.15 2.45 3.30 4.cannot be determined Q4. 300 persons are participating in a meeting in India, out of which 120 are foreigners, and the rest are Indians. Out of the Indians, there are 110 men who are not judges; 160 are men or judges, and 35 are women judges. There are no foreign judges. How many Indian women attended the meeting? 1.60 2.45 3.55 4.40 Q5. Had the CP been 10% less and SP been 10% more, profit % would have been double than that of earlier case. What is the actual CP? 1. Rs.70 2. Rs.100 3.Rs. 140 4.cannot be determined Q6. A train of 100 m long is approaching an unmanned railway crossing. The train is travelling at a uniform speed of 90 km/hr and is 1 km away from the crossing. At the same time, a bus, also approaching the crossing, is 700 m away from it. Assuming the bus is also travelling at a uniform speed of B, at what range of B will the bus collide with the train?(Neglect the length and breadth of the bus) 1. 59.3 km/hr < B < 61.3 km/hr 3. 55.3 km/hr < B < 65.3 km/hr 2. 57.3 km/hr < B < 63.3 km/hr 4. 53.3 km/hr < B < 67.3 km/hr Q7. There are 8 days in a week from Sunday to Saturday and another day called OZ day on planet OZ. There are 36 hrs in a day and each hour has 90 min while each minute has 60 sec. Find the approximate angle between the hands of a clock on OZ when the time is 16:50 am?(The hour hand takes two complete rounds in a day) 1. 189 2. 131 3. 320 4. 165 Directions for questions 8 Read the passage below and solve the questions based on it. Several runners, numbered 1, 2, 3,……. and so on, start simultaneously at the same point on a circular track and run continuously, in the same direction, around the track. They run such that the speed of the runner numbered n (n>1) is n times that of the runner numbered 1. Q8. If there are exactly six runners, then at how many distinct points on the track is the runner numbered 1 overtaken by any of the other five runners? 1. 15 2. 11 3. 9 4. 10 Q9. Three persons A, B and C start running simultaneously on three different concentric circular tracks from three collinear points P, Q and R respectively which are collinear with the centre O and are on the same side of the centre as shown. The speeds of A, B and C are 5 m/s, 9 m/s and 8 m/s respectively. The lengths of the tracks on which A, B and C are running are 400m, 600m and 800 m respectively. If A and B run in clockwise direction and C in anti-clock wise direction, after how much time will the positions of time A, B and C be collinear with the centre (and on the same side of the centre), for the first time they start? 1. 200 seconds 2. 400 seconds 3. 600 seconds 4. 800 seconds Q10. A boss can do a job in two days if his four secretaries A, B, C and D are all present. Their 1 1 1 1 , , , efficiency got reduced to 6 4 3 2 respectively according as A, B, C and D remain absent. In any day only one secretary remains absent. Also the boss finishes his work exactly in integral number of days. Which of the following secretaries cannot be absent for an odd number of days? 1.A 2.B 3.C 4.D Directions for questions 11 Read the passage below and solve the questions based on it. A book containing pages between 4000 and 5000 is divided into four parts, each part being divided into chapters. The total number of pages in each of the four parts is the same. The ratio of the chapters across all the parts is 6:5:10:14. No. of chapters in fourth part is 70. Also each chapter have equal number of pages. Q11. The total number of pages in the book is 1.4000 2.4800 3.4200 4.None of these Q12. Sharat is walking down a descending escalator and takes 40 steps to reach the bottom. Chandra starts simultaneously from the bottom, taking two steps for every one step taken by Sharat. Time taken by Sharat to reach the bottom from the top is same as the time taken by Chandra to reach the top from the bottom. How many steps more than Sharat did Chandra take before they crossed each other on the escalator? 1.20 steps 2. 25 steps 3. 40 steps 4. 60 steps Q13. In 1932, Ramu found that his age is exactly equal to the two-digit number formed by last two digits(i.e. the tens and the units place digit) of his year of birth. Similarly, his grandfather found that in 1932, his age also was equal to the two-digit number formed by the last two-digits of his year of birth. What is the sum of ages of Ramu and his grandfather in 1947? a. 78 years b. 64 years c. 82 years d. 112 years Q14. Sameer marks-up an article by p%(p>0), gives a discount of (p/4)% and gets a profit of (p/4)%. Had he marked up by (p/2)% and given a discount of (p/6)%,What would be his profit percentage? a. 25% b.33.33% c.50% d. not determinable in numerals Q15. Ram and Shyam attended a food festival. Ram gave an order for 3 burgers,4 pasteries and 2 pizzas whereas Shyam placed an order for 2 burgers, a pastry, and 3 pizzas. The bill for Ram and Shyam was Rs.1050 and Rs.950 respectively. If Ram exchanges a Pizza for a Pastry from Shyam, then which of the following is true? a. Shyam owes Ram a sum of Rs. 150 b. Shyam owes Ram a sum of Rs. 100 c. Ram owes Shyam a sum of Rs. 150 d. none of these. Q16. You want to attend a concert by your favourite musician. Unfortunately, you do not reach on time and all the tickets of the concert are sold. However, you find one seller who has an extra ticket and is willing to sell it to you. He offers you the ticket for Rs. 100. You counter by offering Rs. 50. The bargaining starts, he countering by asking the average of the two offers and you countering by the average of your previous offer and the seller’s new offer. The process continues in this manner, until both of you agree on the exact price. At what price will both of you finally agree upon? a. Rs.65.64 b. Rs. 67.64 c. Rs. 66.14 d. Rs. None of these Q17. A bird starts flying from a place A towards C via B. There is no wind resistance from A to B but there is wind resistance between B and C. The bird takes 6 minutes to travel from A to C, whereas it takes 8 minutes to return to A from C. Had there been wind resistance between A and B also, the bird would have taken only 5 minutes to travel from A to C. What would be the time taken by the bird to travel from A to C, if there was no wind resistance between B and C? a. 6.5 min. b. 6.67 min. c. 7 min. d. none of these Q18. Rohan and Sohan start simultaneously from a point A on a circular track and run in the same direction. The speed of Rohan is nine times the speed of Sohan. How many times are they diametrically opposite to each other by the time Sohan completes three complete rounds on the track? a. 27 b. 23 c. 48 d. 24 Q19. x,y,m,n and k are single digit natural numbers( not necessarily distinct) such that (10x+y)2=100m+10n+k. For how many numbers of the form (10x+y) does the following expression hold? (10y+x)2=100k+10n+m a. 3 b. 4 c. 6 d. 8 Q20. Amit has Rs. 80 in denominations of Re.1, Rs.2 and Rs.5. He went to a fare , where he played a shooting game. He paid Re.1 for each attempt and won a Rs. 2 coin for each successful shot. The amount he won is 2/3 times more than what he spent. If at any point of time he had at least 20% of the amount with him in the denominations of Re.1, then find the least possible number of Re.1 coins he had initially. a. 16 b. 23 c. 25 d. 30 Q21. Anshuman left his home by car at )7:00 am for Vilaspur. At 7:30 am, he overtook a truck also travelling towards Vilaspur. He reached Vilaspur and started his journey back home after two hours. One hour after leaving Vilaspur he crossed the same truck. Find the ratio of speed of Anshuman’s car and the truck, if Anshuman crossed the truck for the second time at 1:00 pm. (assume truck didn’t halt during the journey and both the car and truck travelled with constant speeds) a. 9:4 b. 11:3 c. 13:7 d. 5:3 Q30. Only a single rail track exists between station A and B on a railway line. One hour after the north bound super fast train N leaves station A for station B, a south bound passenger train S reaches station A from Station B. The speed of the super fast train is twice that of a normal express train E, while the speed of a passenger train s is half that of E. On A particular day N leaves for station B. From Station A, 20 minutes behind the normal schedule. In order to maintain the schedule both N and s increased their speed. If the super fast train doubles its speed, what should be the ratio (approximately) of the speed of passenger train to that of the super fast train so that passenger train S reaches exactly at the scheduled time at station A on that day (a) 1:3 (b) 1:4 (c) 1:5 (d) 1:6 Q33. Deepak and Anchal both start running around a circular track in the clockwise direction moving at a constant speed. Deepak is on his bike while Anchal is on bicycle. Deepak goes all the way on the track and catches Anchal in the next round. As soon as he meets Anchal he turns back and head towards the starting point while Anchal keeps moving on his path. When Deepak reaches the starting point he again meets Anchal who is just finishing his first round. What is the ratio of their speeds? a) 1:2 b) 1:3 c) 4-sqrt2 : 1 d) 1 + sqrt2 : 1 Q34. Deepak and Manish are moving along two straight roads that intersect perpendicularly at X. When Deepak is at X, Manish is 500m from X. After 2 minutes both Manish and Deepak are at equal distance from X, and after 8 more minutes they are again at equal distance from X. What is the ratio of their speeds? a) 4:5 b) 1:2 c) 2:3 d) 5:8 Q38. 100 students of a class appeared for a test that had 30 questions. Each question carried 1 mark for correct answer and there were no negative markings for wrong answers. The number of students in the class who attempted atleast n questions wrong is given by P = 60 – 2n (n > 0). The average marks of the class can be: a) 27.3 b)87.0 c)21.3 d)data insufficient ANSWER QUEST-39 & 40 BASED ON THE INFORMATION GIVEN BELOWBrett & lee were running from opposite ends of a linear track PQ, Brett from P and Lee from Q simultaneously in opposite directions. The first time they meet each other is at 0.6 PQ from Q. After meeting they continue in their respective directions & continue the same process. Q39. What is the total distance covered by Brett & Lee at the time of their 17th meeting? a)17PQ b)33PQ c)34PQ d)Data insufficient Q40. Till their 10th meeting, how many times have they met at the end points? a)1 b)3 c)4 d)none of these Q41. What is the total distance covered by Lee Till the time of their 22nd meeting? a)25PQ b)25.8PQ c)17.2PQ d)Can’t b determined