Directions (51-55) : In these questions, two equations numbered 1 and Ii are given. You have to solve both the equations and choose the appropriate answer.
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51). I. \( \Large 2x^{2} -15x+28 = 0\)
II. \( \Large y^{2} -7y +12 =0 \)
| A). \( \Large x \ge y \) |
| B). \( \Large x < y \) |
| C). \( \Large x \le y \) |
| D). x=y or relationship between x and y cannot be established |
| E). \( \Large x > y \) |
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52). I. \( \Large 2x^{2} +3x+1 = 0\)
II. \( \Large 8y^{2} +22y +15 =0 \)
| A). \( \Large x \ge y \) |
| B). \( \Large x < y \) |
| C). \( \Large x \le y \) |
| D). x=y or relationship between x and y cannot be established |
| E). \( \Large x > y \) |
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53). I. \( \Large x^{2} -11x+15 = 0\)
II. \( \Large 2y^{2} -17y +35 =0 \)
| A). \( \Large x \ge y \) |
| B). \( \Large x < y \) |
| C). \( \Large x \le y \) |
| D). x=y or relationship between x and y cannot be established |
| E). \( \Large x > y \) |
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54). I. \( \Large 2x^{2} -11x+15 = 0\)
II. \( \Large 2y^{2} -17y +35 =0 \)
| A). \( \Large x \ge y \) |
| B). \( \Large x < y \) |
| C). \( \Large x \le y \) |
| D). x=y or relationship between x and y cannot be established |
| E). \( \Large x > y \) |
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55). I. \( \Large 2x^{2} -15x+27 = 0\)
II. \( \Large y^{2} =9 \)
| A). \( \Large x \ge y \) |
| B). \( \Large x < y \) |
| C). \( \Large x \le y \) |
| D). x=y or relationship between x and y cannot be established |
| E). \( \Large x > y \) |
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Directions (56-60) : Study the following information carefully to answer the given questions.
The total population of three villages A, B and C together is 80,000 and the ratio between their respective populations is 5 : 4 : 7. Out of the total population of Village A, the age of 16% of villagers is equal to 61 years or more, the age of 36% of villagers is equal to or more than 31 years but less than 61 years and the age of the remaining villagers is less than 31 years.
Out of the total population of Village B, the age of one-fifth of villagers is equal to 61 years or more. Out of the remaining population, the age of \( \Large \dfrac{12}{25} \)th villagers is equal to or more than 31 years but less than 61 years and the age of the remaining villagers is less than 31 years.
In Village C, the number of villagers whose age is equal to 61 years or more is 50% more than the difference between the number of villagers in Village A whose age is less than 31 years and that in Village B. The number of villagers whose age is equal to or more than 31 years but less than 61 years is 80% more than that in Village A in the same age group. The age of the remaining villagers is less than 31 years. |
56). In Village C, out of the total population whose total age is equal to 61 years or more, \( \Large \dfrac{1}{6} \)th of the females and out of the total population whose age is equal to or more than 31 years but less than 61 years, one-fifth are females. What is the respective ratio between the number of males whose age is equal to 61 years or more and the number of females whose age is equal to or more than 31 years but less than 61 years ?
| A). 27 : 85 |
| B). 23 : 81 |
| C). 22 : 81 |
| D). 23 : 83 |
| E). 25 : 64 |
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57). In Village A, the respective ratio between the total number of male villagers and the total number of female villagers is 23:27. If \( \Large \dfrac{9}{16} \)th of the total villagers whose age is equal to 61 years or more are females, what percent of female population in Village A is equal to 61 years or more ?
| A). \( \Large 15 \dfrac{1}{3} \) |
| B). \( \Large 18 \dfrac{2}{5} \) |
| C). \( \Large 14 \dfrac{2}{3} \) |
| D). \( \Large 16 \dfrac{2}{3} \) |
| E). \( \Large 13 \dfrac{1}{3} \) |
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58). In Village B, out of the total population, 36% are graduates. If the number of male graduates is 40% more than that of female graduates, females graduates are what percent of the total population?
| A). 15 |
| B). 20 |
| C). 5 |
| D). 25 |
| E). 18 |
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59). What is the average production across the three villages whose age is less than 31 years?
| A). 11500 |
| B). 11750 |
| C). 12500 |
| D). 12700 |
| E). 11200 |
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60). By what pereent the population of village B whose age is equal to or greater than 31 years; is less than the population of village A in the same age group ?
| A). \( \Large 13 \dfrac{3}{17} \) |
| B). \( \Large 14 \dfrac{2}{19} \) |
| C). \( \Large 11 \dfrac{2}{13} \) |
| D). \( \Large 10 \dfrac{2}{13} \) |
| E). \( \Large 12 \dfrac{2}{19} \) |
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