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Chapter – 2 Tests – 2
- A person buys some apples and mangoes from the market at rate such that a mango is twice as costly as an apple and he sells them such that a mango is thrice the price of an apple. By selling an apple at twice of its CP he makes 150% profit on the whole. Find the proportion of mangoes to apples.
- can’t be determined
- Maddy is engaged in two transactions, where he earns same amount as profit in each case. He makes a 25% profit in first transaction and a 20% gain in second. If the same amount is earned as the profit and the 2 transaction are combined, his profit becomes 22.22%. The sale price in the combined transaction is
- can’t be determined
- Each tree in a forest houses at least one bird. On half number of trees there are 2 sparrows each, on 1/4th of the remaining trees there is one pigeon each and the rest, that houses 4 birds each, are cut off for factory use. If there were in all 630 birds in the forest, how many trees were cut off?
- can’t be determined
- The students of three classes A B and C take a test. The average marks of classes A and B put together is 71. The average marks of class B and C put together is 76. The average mark of class A and C put together is 79. Find the range of average marks (P) of all three classes put together.
- 72 < P < 76
- The mileage of a car is 16 km / lt., if the fuel is totally unadulterated. If due to adulteration the mileage reduces by 25%, by what % does the cost of maintaining the car per km increase? (assume that the maintenance cost is equal to the fuel cost)
- The ratio of Ram’s age to the Raghu’s age is same as the ratio of the ages of their respective elder brothers. The ratio of difference of the ages Ram & Raghu to that of the difference of ages of their respective brothers is 1:2. What is the ratio of sum of the ages of their respective brothers to the sum of the ages of Ram and Raghu?
- underroot 2:1
- Three different types of balls priced at Rs.5, Rs.8 and Rs.13 per piece are displayed in 3 different boxes by a trader. Mr. Gopi got from this shop all three types of balls spending a total sum of Rs.768. The numbers of the balls he got taken in the order, in which the prices are mentioned above, are in the ratio 5:4:3. How many balls of the costlier variety did he buy?
- A lump of 2 metal weighing 18gms is worth Rs.87. If their weight be interchanged, it would be worth Rs.78.60. If the price of one metal is Rs.6.7/gm., find the weight of the other metal in the mixture
- A boy finds the average of 10 positive integers. Each integer contains 2 digits. By mistake, the boy interchanged the digits of one number say ba to ab. Due to this, the average becomes 1 8 less than previous one. What was the difference of the two digits a and b
- A Student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6:7:8:9:10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 50% marks is
- A shipping clerk has five boxes of different but unknown weights each weighing less than 100kg. The clerk weighs boxes in pairs. The weights obtained are 110,112,113,114,115,116,117,118,120 and 121. What is the weight of the heaviest box?
- can’t be determined
- 2 lumps of gold, silver and copper together weigh 20kg. 1 lump contains 75% gold and 31.25gm silver/kg. Another lump contains 85% gold and 30gm silver/kg. The total quantity of silver in two lumps is 617.5gm. If two lumps are melted to form one, the % of gold in it will be
- We have 735gms of a 16% solution of iodine in alcohol. We decide to add iodine to get the mixture to 20%. But after 3 days, we find that the solution is already of 20% consistency. How much alcohol would have evaporated off
- A train travels at an average speed of 75km/hr without stoppages, and with stoppages it covers the same distance at an average speed of 60km/hr. How many minutes per hour does the train stop?
- Average age of the students in a class of 50 is 13. the weight of each is directly proportional to the height and the height is also found to be in direct proportion to the age. A student of age 11 is 165 cm tall, with weight being 33 kg. Find the average weight of the class.
- data insufficient
- One man can do as much work in one day as a woman can do in 2 days. A child does one-third the work in a day as a woman. An estate owner hires 39pairs of hands of men, women and children in the ratio 6:5:2 and pays them in all Rs. 1113 at the end of days work. What must the daily wages of child be, if the wages are proportional to the amount of work done?
- Total expenses of running the hostel at Harvard Business School are partly fixed ad partly varying linearly with the numbers of boarders. The average expense per boarder is $70 when there are 25 boarders and $60 when there are 50 boarders. What is the average expense per boarder when there are 100 boarders?
- In a co-educational school there are 15 more girls than boys. If the number of girls is increased by 10% and the number of boys is also increased by 16% there would be 9 more girls than boys. What is the number of students in the school?
- A 6cm long cigarette will burn itself up in 15 min if no puff is taken. For every puff, it burns three times as fast during the duration of the puff. If the cigarette burns itself in 13 min, then how many puffs has the smoker taken if his average puff lasted 3 s?
- An index of 12 shares contains, among others, the shares of Reliance, HLL and Infosys with weightages of 7%, 13%, and 15% respectively. If these 3 rise by 9%, 10%, and 4% respectively, while the index rises by 6%, then what is the increase in the prices of other shares?
- can’t be determined
- A container of 20 litres capacity is completely filled with milk and water mixed in the ratio 3:1. Spherical pebbles of volume 1.0 cc each are dropped into the vessels as a result of which some mixture overflows. The pebbles are removed and water added to replace the mixture that overflowed. On analysis, the new mixture was found to contain only 60% milk. The number of pebbles dropped into the container was
- none of these
- A vessel contains 100kg of two chemicals X and Y mixed in the ratio 7:3 by weight. Their densities are in the ratio of 2:1. When heated, X evaporates @1kg per hour, which is half the rate of evaporation of Y. to obtain a residue with a density 4/3 times that of the original mixture, the number of hours for which the mixture need to be evaporate will be closest to
- The average height of for brothers is 74 inches and the difference in heights of the 2 eldest brothers is 2 inches. The difference between the 2 youngest brothers is 6 inches. Which of the following must be one of the heights?
- According to a plan, a team of woodcutters decide to harvest 216 m3 of wheat in several days. In their first three days, the team fulfilled the daily assignment, and then it harvested 8 m3 of wheat over and above the plan everyday. Therefore, a day before the planned date, they had already harvested 232 m3 of wheat. How many cubic meters of wheat a day did the team have to cut according to the plan?
- One man can do as much work in one day as a woman can do in 2 days. A child does one third the work in a day as a woman. If an estate owner hires 39 pairs of hands-men, women and children in the ratio 6:5:2 –and pays them an all Rs.1113 at the end of the day’s work, what must the daily wages of a child be, if the wages of a child be, if the wages are proportional to the amount of work done?
- There are three containers – M, W and H- of equal capacities, containing milk, water and honey respectively. Each container is filled upto 75% of its capacity. Now, W is topped up, to its brim (i.e. , filled completely), with the content of M, after which , H is topped up, to its brim, with the content of W and at last, the content of H are used to fill M again up to 75% of its capacity. Which among the following statements is true regarding m, w and h, which are the respective concentration of milk in M, water in W and honey in H?
- none of these
- Because of the budget presented by Sinha, the price of sugar increased by 40%. The Mehra family reduced its consumption so that the expenditure on sugar is up only by 12%. If the total consumption of sugar before the rise in price was 50kg. What is the present consumption of sugar (in kg)?
For Q 28-29: The following table represents the salinities of water from different sources relative to river water, whose salinity is taken to be 1.00
Water Sources Salinity
Ground water 0.36
Pond Water 0.64
Lake water 0.88
River water 1.00
Sea water 10.00
Ocean water 40.00
28. What is the minimum amount (in litres) of river water that must be added to 100 litres of ocean water to make a solution, which has at the most four times the salinity of the rive water?
29. A solution is formed by taking lake water river water and sea water in the ratio of 2:3:4. what is the approximate salinity of the solution relative to the river water?
30.I went to a hotel along with 12 friends. I paid Rs.145 and all the others paid an equal amount. In the end when we did some calculation, we found that the average sum paid by all of us was Rs.5 more than what was originally paid by which of my friends. How much money did each of my friends pay?
31. Anup brought three cylindrical ice-cream packs whose radii are in the ratio 2:3:4. He has to carry them home. The rate at which the temperature of each pack increases varies directly as the lateral surface area and varies inversely as the volume of the container. He has an insulting flask which can be used to enclose exactly one of the three packs. If he wants, to keep in the flask that pack whose temperature falls at the fastest rate, which pack must he keep in the flask?
a. first pack
b. second pack
c third pack
d. can’t be determined
For Q 32-33: Answer the question based on the following information
There are two vessels-one is in the shape of a cylinder and the other in the shape of a right circular cone. Both the vessels have the same height and the same base radius. The cylindrical vessel and the conical vessel are filled with milk and water respectively and are both filled to half their maximum heights. The cone is standing on its vertex
32. The contents of the conical vessel is emptied into the cylindrical vessel. What is the ratio of water to milk in the cylindrical vessel now?
33. Water is added to the conical vessel taking note that the total volume of water in the cone does not exceed the volume that is the empty in the cylinder. This amount is now emptied into the cylinder. What is the ratio of milk and water in the cylinder now?
For Q 34-35: Answer the question based on the following information
There are 3 cylindrical vessels – A, B, and C- whose heights are same and radii are in the ratio 1:2:3. A contains milk, B contains water, and C contains honey and are filled to capacity. There are three machines which can empty the content of A in 10min, of B in 20 min and of C in 30 min into a fourth vessel D. They are used empty A, B, and C respectively.
34. What is the ratio of milk, water and honey in a mixture formed then the content of the three vessels are emptied by the respective machines all of which started the operation simultaneously?
d. none of these
35. What fraction of D is filled if it is also a cylinder of radius 10 m and the radius of the cylinder is 1m?(All have the same height)
d. none of these
36. The average weight of three men – A, B, and C – is 84kg. A fourth man D joins them and the average weight of these four men becomes 80kg. If E, whose weight is 3 kg more than D, replace A, the average weight of the four men becomes 79kg. The weight of A is
37. A milkman has two cans of capacities 10 L and 20L with milk of concentrations 60% and 70% respectively. If he takes 3 L and 2 L out from different cans, not necessarily in that order of the cans, what is the maximum milk concentration of the mixture taken out?
38. A fuel is half filled with petrol A. Then it is filled with petrol B up to half of the remaining volume of the tank. Half of the remaining portion is filled with A. Half of the rest is filled with B. the process is continued till the tank is filled. What is the ratio of volume A and B, when the tank is fully filled up?
d. cannot be determined
39. If 50% of a 2:3 solution of milk and water is replaced with water, the concentration of the solution is reduced by
40. The height of Rajan is of the same proportion as the square root of his age (between 5 and 17). What will be the height of Rajan after 7 years, if he is 4 ft tall at the age of 9years?
a. 4ft 5inches
b. 5ft 4inches
c. 6ft 5inches
d. 5ft 6inches
41. The concentration of an acid solution is inversely proportional to the volume of the solution if the amount of acid is not changed. A 40% hydrochloric acid solution becomes 30% solution when 20 L of water is added to it. Find the original volume of the solution.
a. 80 L
b. 70 L
c. 90 L
d. 60 L
42. three pipes of varying diameter can fill the vessel of 1, 2 and 3 L in 4, 18 and 48 min respectively. What is the ratio of their diameter?
43. Two cogged wheels, one has 16 cogs and the other has 27, work into each other. If the second wheel turns 80 times in three quarter of a minute, how often does the other turn in 8 s?
a. 24 turns
b. 25 turns
44. p, q and r are three positive numbers and Q= (p+q+r)/2. If (Q-p): (Q-q): (Q-r)=2:5:7, then find the ratio of p, q, and r?
45. Rs.535 is divided by among A, B and C so that if Rs.15, Rs.10, Rs.30 be subtracted from their respective shares, the remainders may be in the ratio4:5:7. What was their initial share (in Rs.)?
a. 120, 145,220
b. 125, 150, 225
c. 130, 155, 230
d. 135, 160, 240
46. A mixture of certain quantity of milk with 16L of water is worth 90 paise per litre. If pure milk costs 108 paise per litre, what is the amount of milk in water? (Assume that water does not cost anything)
47. 27 L of orange juice contains 312 calories and 9 L of mango juice contains 54 calories. If 18 L of mixture of both orange and mango juice contains 118 calories. Find the proportion of orange juice in the mixture.
48. Fresh grapes contain 90% water by weight while dried grapes contain 20% water by weight. What will be the weight of dry grapes available from 20kg of fresh grapes?
49. A batsman scored an average of 55 runs in the first 6 test. If the first test is not counted and the seventh is counted then his average score goes up to 57. If the score in the first test was 50 runs, find his score in the seventh test.
50. The average score of 55 students in an examination is 88. if the score of the top four students is not considering then the average of the remaining students drops by 4, if the second highest score ranker scored less than 133 and all the students have got integral scores, find the minimum marks that could have been scored by the topper.
d. can’t be determined