Q1. If the work done by (x-1) men in (x+1) days is to the work done by (x+2) men in (x-1) days is in the ratio 9 : 10, then the value of x is Q2. One year ago the ratio between Laxman’s and Gopal’s salary was 3 : 4. The ratios of their individual salaries between last year’s and this year’s salaries are 4 : 5 and 2 : 3 respectively. At present the total of their salary is Rs 4160. The salary of Laxman now, is: Q3. Rs 385 has been divided among A, B, C in such a way that A receives 2/9th of what B and C together receive. Then, A’s share is: Q4. Five apples and 4 pears cost as much as 7 pears and 3 apples. Find out the ratio of the cost of one apple to the cost of one pear Q5. Calculate the weight and the percentage of zinc in the zinc-copper alloy being given that the latter’s alloy with 3 kg of pure zinc contains 90 per cent of zinc and with 2 kg of 90% zinc alloy contains 84% of zinc. Q6. The average age of 3 girls is 20 years and their ages are in the proportion 3 : 5 : 7. The age of youngest girl is: Q7. 94 is divided into two parts in such a way that fifth part of the first and eighth part of the second are in the ratio 3 : 4. The first part is: Q8. A person covers half of his journey from delhi to Mathura by terrain at 60 km/hr. Half the remainder by bus at 30 km/hour and rest by cycle at 10 km/hr. Find the average speed during the entire journey? Q9. The ratio of marks obtained by vinod and Basu is 6:5. If the combined average of their percentage is 68.75 and their sum of the marks is 275, find the total marks for which exam was conducted. Q10. The ratio of boys to girls at a school disco is 9:10. An extra 17 boys arrive and the ratio changes to 8:7. How many girls are there at the disco? Q11. Three jackals P , M and T together have 675 loaves of bread. P has got three times as M but 25 loves more than T. How many does T have ? Q12. Two solutions of 90% and 97% purely are mixed resulting in 21 lts. Of mixture with 94% purity. How much is the quantity of the first solution in the resulting mixture? a. 10lts b. 15lts c. 9lts d. None


Q1. Brass is an alloy of copper and zinc. Bronze is an alloy containing 80% copper, 4% of zinc and 16% of tin. A fused mass of brass and bronze is found to contain 74% of copper, 16% zinc, and 10% of tin. The ratio of copper to zinc in brass is Q2. The time period of a pendulum varies directly with the square root of the length of the pendulum and inversely as the acceleration due to gravity. If the length of the pendulum is made four times the original and the acceleration due to gravity is halved, then what is the ratio of the time periods of the pendulum in the two cases? a. 1 b.1/4 c. 1/16 d. 1/8 Q3. The length of a rectangle is increased by 30% and its width is decreased by 10%. This increases the area by: a. 20% b. 15% c. 22% d. 17% e. None of these Q4. The radius of the circum circle of an equilateral triangle of side 12 cm is. Q5. Harsha used 6 lts of oil to paint the map of India 6 mts high. How many liters of paint would be need for painting for proportionately scaled map of 18 mts high. Q6. Two jars having a capacity of 3 and 5 liters respectively are filled with mixtures of milk and water. In the smaller jar 25% of the mixture is water. The jars are emptied into a 10 liter cask whose remaining capacity is filled up with water. Find the percentage of milk in the cask. Q7. The areas of two spheres are in the ratio 1 : 4. The ratio of their volumes is Q8. What is the maximum value of x/y for which (x-2) 2 = 9 and (y-3) 2 = 25 ? Q9. If a, b and c are all real numbers, the minimum value of ab + bc + ca is a. 0 b. –1/2 c. –3/2 d. None Q10. The monthly salaries of two persons are in the ratio of 4:7. If each receives an increase of Rs.25 in the salary, the ratio is altered to 3: 5. Find their respective salaries. END


Q1. If a and b are positive integers then 2 always lies between i. (a+b)/(a-b) and ab ii. a/b and (a+2b)/(a+b) iii. a and b iv. ab/(a+b) and (a-b)/ab Ans: ii Q2. X and Y are positive integers and it is given that X is less than Y. If X2+ Y2 equals two times 5, the X/y= ? ANS: 1/3 Q3. The sides of triangle are in the ratio 1/3 : ¼ : 1/5 and its perimeter is 94 cm, the length of smallest side is: ANS: 31.3 cm Q4. An alloy of gold and silver is taken in the ratio 1 : 2, and another alloy of the same metals is taken in the ratio of 2 : 3. How many parts of the two alloys must be taken to obtain a new alloy consisting of gold and silver that are in the ratio 3 : 5? Ans: 3 and 5 Q5. The proportion of milk and water in 3 samples is 2:1, 3:2 and 5:3. A mixture comprising of equal quantities of all 3 samples is made. The proportion of milk and water in the mixture is ANS: 227:133 Q6. The weights of three heaps of gold are in the ratio 5: 6: 7. By what fractions of themselves must be the first two be increased so that the ratio of the weights may be changed to 7: 6: 5? Ans: 24/25, 2/5 Q7. A mixture contains milk and water in the ratio 5:1. On adding 5 lts of water the ratio of milk and water becomes 5:2. Find the quantity of milk in the original mixture ANS: 25lts Q8. The radius of the circum circle of an equilateral triangle of side 12 cm is. ANS: 4√3 cm Q9. Starting at 870 and counting backwards by 7’s, a student count 870, 863, 856, etc. A number that will be counted is: a. 116 b. 115 c. 114 d. 113 e. 112 Q10. Two numbers are such that their difference, their sum and their product are in the ratio of 1 : 7 : 24. The product of the numbers is ANS: 48 Q11. A second order recurrence relation is defined by un+1 = (un+un 1)/2; that is, each new term is the mean of the previous two terms.For example, when u1=2 and u2=5, we generate the following sequence: 2, 5, 3.5, 4.25, 3.875, Find the limit of the sequence for different starting values.


Q1. The monthly incomes of A and B are in the ratio 4: 5; their expenses are in the ratio 5: 6. If 'A' saves Rs.25 per month and 'B' saves Rs.50 per month, what are their respective incomes? Q2. x varies with y then x2 + y 2 varies as i. x + y ii. X - y iii. x2 + y 2 iv. None Q3. N and A can do a work in 10 days and N alone in 12 days. In how many days can the work be done by 6 boys and 11 women together. Q4. The marks scored by a student in three subjects are in the ratio of 4 : 5 : 6. If the candidate scored an overall aggregate of 60% of the sum of the maximum marks and the maximum marks in all three subjects is the same, in how many subjects did he score more than 60%? Q5. If a lies between 2 and 3, both included, b lies between 4 and 6, both included, then what is the ratio of minimum and maximum limits of a2 - b2 ? Q6. A group of workers can do a piece of work in 24 days. However as 7 of them were absent it took 30 days to complete the work. How many people actually worked on the job to complete it? Q7. The proportion of milk and water in 3 samples is 2:1, 3:2 and 5:3. A mixture comprising of equal quantities of all 3 samples is made. The proportion of milk and water in the mixture is Q8. A, B and C, each of them working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn Rs.2340, what ill be C's share of the earnings? Q9. Two solutions, the first of which contains 0.8 kg and the second 0.6 kg of salt, were poured together and 10kg of a new salt solution were obtained. Find the weight of the first and of the second solution in the mixture if the first solution is known to contain 10 percent more of the salt than the second Q10. A solider was awarded for each wound inflicted upon a battle. For thr first wound he was awarded Re 1, for the second Rs.2 , for the third Rs. 4 and for the fourth Rs.8 and so on. He received in total Rs. 65,535. Find the wounds he received. Q11. Two varieties of wheat are mixed in the proportion of 3:2 and the mixture is sold at Rs 11 per kg at 10% profit. If the first Varity of wheat costs Rs. 2 more per kg than the second, what does it costs per kg? ANS: Rs. 10.80 Q12. It is 185 miles from Birghamton to New York City. If the bus takes 2 hours to travel the first 85 miles, how long must the bus take to travel the final 100 miles so as to average 50 miles an hour for the entire trip? ANS: 102 min END


Q1. A bag contains 25 paise, 50 paise and 1 Re. Coins. There are 220 coins in all and the total amount in the bag is rs. 160. If there are thrice as many 1 Re. Coins as there are 25 paise coins, then what is the number of 50 paise coins? Q2. 6 men, 8 women and 6 children complete a job for a sum of Rs 950. If their individual wages are in ratio 4 : 3 : 2, the total money earned by the children is: Q3. if 3x + 4y : x + 2y = 9 : 4, then 3x + 5y : 3x - y is equal to ? Q4. In the famous Bhojpur Island, there are four men for every three women and five children for every three men. How many children are there in the island if it has 531 women? Q5. Bob invested his money in high tech stocks. The value of his investment increased by 1/2 . He withdrew all his holdings, spent 3/5 of it, and invested the remainder in blue chip stocks. The value of this investment increased by 4/10. The value of his present holdings is what fraction of the original investment in high tech stocks? Q6. The average age of X and Y is 20 years. If z replaces X the average would be 19 and if Z were to replace Y then the average would be 21.What is the age of Y ? Q7. A, B and C enter into a partnership by investing Rs.3600, Rs.4400 and Rs.2800. A is a working partner and gets a fourth of the profit for his services and the remaining profit is divided amongst the three in the rate of their investments. What is the amount of profit that B gets if A gets a total of Rs. 8000? Q8. A piece of diamond is broken into 3 pcs. The weight of 3 pcs. In the ratio of 1:2:3. Price of piece of diamond is proportional to the square of its weight. Find the price of the original piece, if loss due to breaking is Rs.21000. Q9. The ratio between the ages of Kamla and Savitri is 6 : 5 and the sum of their ages in 44 years. The ratio of their ages after 8 years will be: Q10. The monthly salary of A, B, C is in the proportion of 2 : 3 : 5. If C's monthly salary is Rs 1200 more than that of A, then B's annual salary is Q11. Two liters of a mixture of wine and water contains 12% water. They are added to 3 liters of another mixture containing 7% water, and half a litre of water is then added to whole. What is the percentage of water in resulting concentration? Q12. A fort has provisions for 60 days. If after 15 days 500 men strengthen them and the food lasts 40 days longer, how many men are there in the fort? END


Q1. Determine the smallest number that has exactly 18 factors and is divisible by 30. Q2. A sum of money is divided among A, B, C so that to each rupee A gets, B gets 65 paise and C gets 35 paise. If C's share is Rs 28, the sum is: Q3. Concentration of three wines A, B and C are 10%, 20% and 30% respectively. They are mixed in the ratio 2: 3: x resulting in a 23% concentration solution. Find x? Q4. Rs.432 is divided amongst three workers A, B and C such that 8 times A's share is equal to 12 times B's share which is equal to 6 times C's share. How much did A get? Q5. The expenses of an all boys' institute are partly constant and partly vary as the number of boys. The expense were Rs. 10,000 for 150 boys and Rs. 8400 for 120 boys. What will be the expenses be when there are 330 boys? Q6. The speeds of three cars in the ratio 3 : 4 : 5. The ratio between times taken by them to travel the same distance is: Q7. 24-carat gold is pure gold. 18-carat gold is 3/4 gold and 20-carat gold is 5/6 gold. The ratio of pure gold in 20-carat gold to pure gold in 18-carat gold is Q8. If p + q = 2 and the ordered pair ( p, q ) satisfies 3p + 2q = 1, then the values of p and q are respectively Q9. A bag contains rupees , half ruppe and ten paise coins. The rupee and half rupee coins are in the ratio 2 : 5 and half rupee and ten paisa coins are in the ratio 4 :9. If the total amount is Rs. 1125 find number of ten paise coins. Q10. The sum of two numbers is 11. Their difference is 12. What is their product? Q11.Two containers contain mixture of milk and water in the ratio 5 : 2 and 8 : 5 respectively. Find the ratio in which these mixtures are to be mixed to get a new mixture containing milk and water in the ratio 9 : 4? Q12. The monthly incomes of A and B are in the ratio 4 : 5, their expenses are in the ratio 5 : 6. If 'A' saves Rs.25 per month and 'B' saves Rs.50 per month, what are their respective incomes? ANS: Rs.400 and Rs.500 END


Q1. A mixture contains milk and water in the ratio 5 : 1. On adding 5 litres of water, the ratio of milk and water becomes 5 : 2. The quantity of milk in the mixture is: Q2. The ages of Vivek and Sumit are in the ratio 2 : 3. After 12 years, their ages will be in the ratio 11 : 15. The same of Sumit is: Q3. Rs. 500 are to be divided among A, B, C and D. A and B together get thrice as much as C and D together, B gets 4 times of what C gets and D gets 1.5 times as much as C gets. Find the share of A. Q4. A mixture contains brandy and water in the ratio 8 : X. When 33 lts of mixture and 3 lts of water are mixed the ratio brandy and water becomes 2 :1. The value of X is Q5. In two alloys, aluminum and iron are in the ratios of 1:4 and 1:3. After alloying together 10kg of the first alloy, 16 kg of the second and several kilograms of pure almunium, an alloy was obtained in which the ratio of almunium to iron was 3:2. Find the weight of the new alloy Q6. Two boxes A and B were filled with a mixture of rice and dal .in A in the ratio 5 : 3, and in B in the ratio of 7:3. What quantity must be taken from the first to form a mixture that shall contain 6kg of rice and 3 kg of dal? Q7. One-fourth of the boys and three-eights of the girls in a school participated in the annual sports. What fractional part of the total student population of the school participated in the annual sports? Q8. The prices of a scooter and a television set are in the ratio 3 : 2. If a scooter costs Rs 6000 more than television set, the price of the television set is: Q9. If 2A = 3B and 4B = 5C, then A : C is. Q10. The present ages of A and B are as 6 : 4. Five years ago their ages were in the ratio 5 : 3. Find their present ages. Q11.Bag A contains m coins of 50-paisa and n coins of 25-paisa. Bag B contains m coins of 25-paisa and n coins of 50-paisa. If 3 coins of 50-paisa from bag A are put into bag B and 3 coins of 25-paisa from bag B are put into bag A, the total value in each bag is the same. What is the minimum value of the money in Bag A initially? Q12.A number is a summation of three parts in the ratio 1:2:7 where the largest part is 49. This number is Q13.If x : y = 4 : 5, find the value of (6x + 3y) : (2x + y) Q14. A's money is to B,s money as 4 : 5 and B's money is to C's money as 2 : 3. If A has Rs 800, C has: Q15. If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 hours a day, how many men working with 6 women and 2 boys take to do a job four times as big working for 5 hours a day for 12 days? Q16. The ratio of father's age to his son's age is 4 : 1. The product of their ages is 196. The ratio of their ages after 5 years will be: Q17. If yz : zx: xy = 1 : 2 : 3, then find x/yz : y/xz Q18. A precious stone weighing 35 grams worth Rs. 12, 250 is accidentally dropped and gets broken into two pieces having weights in the ratio of 2 : 5. If the price varies as the square of the weight then find the loss incurred END