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1. I. a^{2} - 13a + 42 = 0, II. b^{2} - 15b + 56 = 0 to solve both the equations to find the values of a and b?
2. If the price has fallen by 10% what percent of its consumption be: increased so that the expenditure may be the same as before?
3. A family consists of grandparents, parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?
4. Ten years ago, the age of Anand was one-third the age of Bala at that time. The present age of Bala is 12 years more than the present age of Anand. Find the present age of Anand?
5. The third proportional to 1 and 2 is?
6. In a colony of 70 residents, the ratio of the number of men and women is 4 : 3. Among the women, the ratio of the educated to the uneducated is 1 : 4. If the ratio of the number of educated to uneducated persons is 8 : 27, then find the ratio of the number of educated to uneducated men in the colony?
7. If cost of sugar increases by 25%. How much percent consumption of sugar should be decreased in order to keep expenditure fixed?
8. The average of first 10 even numbers is?
9. The average of 35 numbers is 25. If each number is multiplied by 5, find the new average?
10. A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year?
11. The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
12. The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
13. Sum of two numbers is 15. Two times of the first exceeds by 5 from the three times of the other. Then the numbers will be?
14. How many figures are required for numbering the pages of a book containing 1000 pages?
15. An automobile financier claims to be lending money at S.I., but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes?
16. The distance between Delhi and Mathura is 110 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?
17. Ravi purchased a refrigerator and a mobile phone for Rs. 15000 and Rs. 8000 respectively. He sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 10 percent. Overall he make a.
18. Find the number of ways of arranging the letters of the word "MATERIAL" such that all the vowels in the word are to come together?
19. In how many ways can three consonants and two vowels be selected from the letters of the word "TRIANGLE"?
20. How many numbers up to 500 are divisible by 23?
21. The number of sequences in which 7 players can throw a ball, so that the youngest player may not be the last is -.
22. A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
23. Simplify : (y^{4b-a} . y^{4c-b} . y^{4a-c}) / (y^{a} . y^{b} . y^{c})^{3}
24. A car started running at a speed of 30 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 10 hours of the journey.
25. In a colony of 70 residents, the ratio of the number of men and women is 4:3. Among the women, the ratio of the educated to the uneducated is 1:4. If the ratio of the number of education to uneducated persons is 8:27, then find the ratio of the number of educated and uneducated men in the colony?
26. 106 * 106 - 94 * 94 = ?
27. A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old id the mother at present?
28. Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
29. Find the one which does not belong to that group ?
30. The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is:
31. The population of a town is 45000; 5/9th of them are males and the rest females 40% of the males are married. What is the percentage of married females?
32. (a^{-3} b^{-2} / a^{2} b^{2})^{-3} * (a^{3} b^{-4} / a^{-3} b^{3}) / (a^{-2} b^{3}/a^{-4} b^{-3}) = ?
33. A sum of money becomes triple itself in 5 years at simple interest. How many years will it become six times at the same rate?
34. Five years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 48 years. What will be the age of the B ten years hence?
35. In a hostel there were 100 students. To accommodate 20 more students the average is decreased by rupees 5. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?
36. The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is:
37. A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is?
38. 96 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?
39. Simple interest on a sum at 4% per annum for 2 years is Rs.80. The C.I. on the same sum for the same period is?
40. Find the one which does not belong to that group ?
41. Find the average of the first 20 natural numbers?
42. Rs. 800 becomes Rs. 956 in 3 years at a rate of S.I. If the rate of interest is increased by 4%, what amount will Rs. 800 become in 3 years?
43. The sides of a triangle are in the ratio 5: 12: 13 and its perimeter is 300 m, its area is?
44. Compound interest earned on a sum for the second and the third years are Rs.1200 and Rs.1440 respectively. Find the rate of interest?
45. The proportion of copper and zinc in the brass is 13:7. How much zinc will there be in 100 kg of brass?
46. A can do a piece of work in 12 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work?
47. If 12 men and 16 boys can do a piece of work in 5 days and 13 men together will 24 boys can do it in 4 days. Compare the daily work done by a man with that of a boy.
48. A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
49. By selling 99 pens, a trader gains the cost of 33 pens. Find his gain percentage?
50. A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount was offered?