2008_Paper V

SAE-1062008 PAPER V Time: 3 Hours Max. Marks: 150 Note: (i) Answer all 15 questions and each question carries 10 marks (15 × 10 = 150 marks). (ii) Give the steps of calculation in each question. (iii) Calculators, not programmable, are allowed in the examination. SECTION I 1. A given machine is assumed to depreciate 40% in value in the first year, 25% in the second year and 10% per annum for the next three years, each percentage being calculated on the diminishing value. What is the average percentage of depreciation, reckoned on the diminishing value for the five years? 2. Three persons A, B and C were given the job of finding the average of 5,000 numbers. Each one did his own simplification. A's method: Divide the set into sets of 1,000 each, calculate the average in each set and then calculate the average of these averages. B's method: Divide the set into 2,000 and 3,000 numbers, take average in each set and then take the average of the averages. C's method: 500 numbers were unities. He averaged all other numbers and then added one. Are these methods correct? 3. If you travel at a constant speed of 20 KMPH from A to B and from B to A at 60 KMPH, what is your average speed? Suppose that your friend travels for half an hour from X to Y at a constant speed of 30 KMPH and from Y to Z for one and a half hours at 40 KMPH. What is your friend's average speed? 4. In a class of 50 students, there are 30 boys and 20 girls. In a test, the average marks obtained by boys was computed to be 40 and those by girls to be 45. However, on scrutiny, it was found that the marks obtained by one of the boys was wrongly taken as 30 instead of 60 and the marks obtained by one of the girls was taken as 70 instead of 50. Find out the correct average marks for the boys and for the girls and for the class as a whole. 5. Lives of two models of refrigerators turned in for new models in a recent survey are given in the following table: Life (No. of years) Model A Model B 0-2 5 2 2-4 16 7 4-6 13 12 6-8 7 19 8-10 5 9 10-12 4 1 Using averages, which model do you recommend to buy? Why? SECTION II 6. In a trip organised by a college there were 80 persons, each of whom paid Rs. 15.50 on an average. There were 60 students, each of who paid Rs. 16. Members of the teaching staff were charged at a higher rate. The number of servants was 6 (all males) and they were not charged anything. The number of ladies was 20% of the total of which one was a lady staff member. Tabulate the above information and fill the blanks in the table, if any. 7. Educational Levels in Two Cities X and Y City:X City:Y Post graduate Post graduate Graduate 27% Under graduate 34% 36° Shool level Shool level 25% 180° Graduate 90° Under graduate Answer the following questions based on the above chart: (a) If there are 70 post graduates in City: X, What is the population of City: X? (b) What percent of the population in City: Y is at school level? (c) If the ratio of the number of graduates in City: X to those in City: Y is 0.45, what is City: Y's population? (d) What is the proportion of students at graduate and post graduate level in cities X and Y taken together? (e) Which educational level is the least in City: Y? 8. Cement Consumption in India (figures in million tons) 55 45 45 30 15 20 Northern region 2001 25 25 Southern region Western region 2002 Eastern region Answer the following questions based on the above chart: (a) In India, how much more cement was consumed in 2002 than in 2001 (in million tons)? (b) Which region showed the highest percentage increase from 2001 to 2002? (c) What is the average consumption of cement per region in 2001 (in million tons)? (d) What is the approximate percentage decrease of cement consumption in the Eastern region for the period 2001-2002? (e) In 2002, if the India's population was 67.5 crore, what was the per capita cement consumption in 2002? 9. Brand Sales in 2002 Percentage Change from earlier year A 7.5 12% B 10 3% C 22 -5% D 34 -10% E 16 -20% Answer the following questions based on the above table: (a) Sales of brand C in 2002 was what the percentage of 2001 sales? (b) The ratio of sales of D in 2002 to E sales in 2002 is ........... (c) What is the proportion of sales of A, B and C to the total sales of all brands in 2002? (d) By how much have the sales of D and E together fallen in 2002 as compared to 2001? (e) Which brand faced the maximum change in sales from 2001 to 2002? Two Products of a Firm 10. 1.5 19 1.0 18 1.09 1.0 17 16 15 16.67 0.6 15.52 2001-2002 2002-2003 2003-2004 Product - A Product - B 0.5 Product-B(%) Product-A(%) 20 Answer the following questions based on the above chart: (a) If in 2003 - 2004, Product-A is 16% more than the previous year, what is its value in 2003 - 2004? (b) What is the average annual growth rate of Product-B during 2001 - 2002? (c) If Product B in 2002 - 2003 is 19% less than the Product-B in 2003 - 2004, what is its value? (d) During which year is Product-A/ Product-B, the maximum? (e) If Product-B in 2002 -2003 has increased by 60% from 2000 - 2001, what is the ratio of Product-B in 2000 - 2001 to Product-A in 2001 - 2002? SECTION III 11. Each of the following is a sequence of numbers that follows a definite pattern. Fill in the blanks to complete the sequence without breaking the pattern. (a) 10001, 10100, 10111, .........., 11101 (b) 13, 22, 39, ............, 137 (c) .............: 14 :: 22 : 32 (d) 13, 32, 87, .........., 737 (e) NAOB, PCQD, .........., TGUH 12. (a) If LADY is coded as B6A1B2A13 then find the code of INDIA. (b) If THURSDAY is coded as VJWTUFCA then decode JQPGUVA. (c) AODR is the code for ROAD, then the code of HUMANITY is .......... (d) Find the odd-man out of the series: 2007, 999, 499, 243, 117, 54 (e) If MANGO = 20 and PINEAPPLE = 44, then what is the value of ORANGE? 13. (a) Find the day on 24th May, 1984. (b) At what time between 4o' clock and 5o 'clock will the minute hand and the hour hand be perpendicular to each other? (c) Four doctors Laxman, Lala, Lazar and Laxmi and four engineers Murali, Murari, Mukund and Mamatha are sitting around a table. No two doctors sit adjacent to each other. Laxmi is two places to the right of laxman and adjacent to Mamatha, who is two places to the left of Murali, who is adjacent to Laxman. If Murari is seated three places to the left of Lala, then Murari is seated between which two persons? 14. People in twin cities are facing the problem of traffic jams frequently everywhere. You are asked to investigate and submit a brief report on the reasons for traffic jams. Suggest suitable solutions to prevent the traffic jams, explaining the parameters on which you propose to collect data. 15. Smoking, consuming high-calorie fast food and alcohol, will not only cut short life-span but will also cost the country dear. A report jointly prepared by WHO and the WEF says India will incur an accumulated loss of $ 236.6 billion by 2015 due to unhealthy lifestyle and faulty diet. The resultant chronic diseases like heart disease, paralytic stroke, cancer, diabetes and respiratory infections will severely affect people's earnings. The income loss to India due to these diseases, which was $ 8.7 billion in 2005, is estimated to rise to $ 54 billion in 2015. It is much more in China. According to a report by World Health Assembly (WHA), 60% of all deaths worldwide in 2005, i.e. 35 million deaths resulted from non-communicable diseases (NCDs) and accounted for premature deaths. This number is likely to rise to 47 million deaths in a year, in the next 25 years. What is worrying is around 80% of these deaths will occur in low and middle income countries like India? Almost half of those who will die from chronic diseases will be in their productive years. The cost to employers of morbidity attributed to NCDs is increasing rapidly Work-places should make possible healthy food choices and support physical activity. Unhealthy diet, excessive energy intake, physical inactivity and tobacco use are major risk factors for NCDs. The study cited scientific evidence that healthy diet and adequate physical activity at least 30 minutes per day for at least five days a week helped to prevent NCDs. In India, 10% of adults suffer from hypertension while the country is said to have 25-30 million diabetics. 3 out of 1000 people suffer from a paralytic stroke. The number of deaths from heart attack is projected to increase from 1.2 million to 2 million in 2010. Let us prevent this situation and make India more healthy. Answer the following: (i) What is the main problem of the above passage? (ii) What are the major risk factors for getting non-communicable diseases? (iii) What are the preventive measures for non-occurrence of non-communicable diseases? (iv) What is meant by productive years? (v) What is the expected income loss to India in 2015? (ûÁ©’í∫’ ņ’-¢√ü¿-´·) Ææ÷îª-†©’: (i) ¢Á·ûªhç 15 v°æ¨¡o-©èπ◊ ûª°æp-E-Ææ-Jí¬ Ææ´÷-üμΔ†ç v¢√ߪ’çúÕ. v°æA v°æ¨¡oèπ◊ 10 ´÷®Ω’\©’ (15 10 = 150 ´÷®Ω’\©’). (ii) v°æA v°æ¨¡o-™†’ í∫ù† NüμΔ-†-´·†’ N¨¡-D-éπ-Jç-°æ¤´·. (iii) v§Òví¬´· -îÁߪ’u-™‰E í∫ù-†-ߪ’ç-vûª-´·-©†’ (é¬u-Lèπ◊u-™‰-ô®˝) °æK-éπ~™ ņ’-´’-Aç-îÁ-ü¿®Ω’. $ ¶μ«í∫´· I 1. 2. 3. 4. äéπ ߪ’çvûª´· N©’´ ¢Á·ü¿öÀ Ææç´-ûªq-®Ω-´·™ 40], È®çúø´ Ææç´-ûªq-®Ω´· 25], ûª®√yûª ´‚úø’ Ææç´-ûªq-®Ω-´·-©™ Ææç´-ûªq-®√-EéÀ 10] ¢Ë’®Ωèπ◊ ûªT_-†îÓ, Å®·ü¿’ Ææç´-ûªq-®√-©™ Ææ®√-ÆæJ ûªí∫’_-ü¿© ¨»ûªç áçûª? Éîªaô v°æA ¨»ûª´· ûªí∫’_-ü¿© N©’-´-°j† í∫ùÀç-îª-•-úÕ-çC. ´·í∫’_®Ω’ ´uèπ◊h©’ A, B ´’Jߪ· C ©èπ◊ 5,000 Ææçêu© ßÁ·éπ\ Ææ®√-Ææ-JE éπ†’-í̆’ °æEE Éî√a®Ω’. v°æA-¢√®Ω’ Åûª-úÕ ßÁ·éπ\ Ææ÷éÃ~ t-éπ-®Ω-ù °æü¿l¥-AE ¢√-ú≈®Ω’. A ßÁ·éπ\ °æü¿l¥A: É*a† ÆæN’-AE, v°æA-üΔ-E™ 1,000 Ææçêu©’ í∫© ÆæN’-ûª’-©’í¬ N¶μº->ç-´·. v°æA ÆæN’A ßÁ·éπ\ Ææ®√-ÆæJ éπ†’-íÌ-†’´· ´’Jߪ· OöÀ ßÁ·éπ\ Ææ®√-Ææ-JE éπ†’-íÌ-†’´·. B ßÁ·éπ\ °æü¿l¥A: 2,000 ´’Jߪ· 3,000© Ææçêu-©’- í∫© È®çúø’ ÆæN’-ûª’-©’í¬ É*a† ÆæN’AE N¶μº->ç-´·. Ñ ÆæN’-ûª’© Ææ®√-Ææ-®Ω’-©†’ éπ†’-íÌ-†’´· ´’Jߪ· OöÀ ßÁ·éπ\ Ææ®√-Ææ-JE éπ†’-íÌ-†’´·. C ßÁ·éπ\ °æü¿l¥A: É*a† ÆæN’-A™ 1 ÅØË Ææçêu 500 ≤ƒ®Ω’x Ö†o-ü¿-†’-éÌ-†’´·. N’T-L† Ææçêu© Ææ®√-Ææ-JE éπ†’-íÌE DEéÀ 1E èπÿ-ú≈úø’. Ñ °æü¿l¥-ûª’©’ ÆæJ Å®·-†¢√? F´¤ 20 KMPH ¢Ëí∫çûÓ A †’çúÕ B éÀ ´’Jߪ· B †’çúÕ A éÀ 60 KMPH ¢Ëí∫-´·ûÓ v°æߪ÷-ùÀç-*† F ßÁ·éπ\ Ææ®√-ÆæJ ¢Ëí∫ç áçûª? F N’vûª’úø’ X †’çúÕ Y E Æœn®Ω-´·í¬ 30 KMPH ¢Ëí∫-´·ûÓ v°æߪ÷-ùÀç* Å®Ωl¥-í∫ç-ô™ îË®Ω’-èπ◊-Ø√oúø’. AJT Y †’çúÕ Z éÀ 40 KMPH ¢Ëí∫-´·™ v°æߪ÷-ùÀç* äéπ-öÀ-†o®Ω í∫çô-©™ îË®Ω’-èπ◊-†oîÓ, F N’vûª’úÕ ßÁ·éπ\ Ææ®√ÆæJ ¢Ëí∫ç áçûª? ûª®Ω-í∫-A-™E 50 ´’çC NüΔu-®Ω’n-©™ 30 ´’çC ¶«©’®Ω’ ´’Jߪ· 20 ´’çC ¶«L-éπ©’ ÖØ√o®Ω’. äéπ-°æ-K-éπ~™, ¶«©’®Ω Ææ®√-ÆæJ ´÷®Ω’\©’ 40 ´’Jߪ· ¶«L-éπ© Ææ®√-ÆæJ 45. ûª®√yûª, äé𠶫©’úÕ ´÷®Ω’\©’ 60éÀ •ü¿’-©’í¬ 30 ´’Jߪ· äé𠶫Léπ ´÷®Ω’\©’ 50éÀ •ü¿’-©’í¬ 70 ûª°æ¤pí¬ BÆæ’èπ◊Ø√o®Ω’. ¶«©’®Ω’ ´’Jߪ· ¶«L-éπ© ÆæJ-ߪ’í∫’ Ææ®√-Ææ-®Ω’-©†’ ´’Jߪ· ûª®Ω-í∫A Ææ®√-Ææ-JE éπ†’-í̆’´·. 5. Ñ véÀçC °æöÀd-éπ™ ÉöÃ-´L ÆæÍ®y v°æé¬-®Ω´· È®çúø’ †´‚-Ø√© -Jv°∂œ->-Í®-ô®Ωx @Nûª 鬩-´·©’ É´y•-úÕ-†N. @N-ûª-é¬-©´·(Ææç´-ûªq-®Ω-´·-©™) †´‚Ø√ A †´‚Ø√ B 0-2 5 2 2-4 16 7 4-6 13 12 6-8 7 19 8-10 5 9 10-12 4 1 Ææ®√Ææ-®Ω’-©†’ Ö°æ-ßÁ÷-Tç*, à †´‚-Ø√†’ é̆’-ôèπ◊ Æœ§∂ƒ-®ΩÆæ’ îËߪ·-ü¿’´¤? áçü¿’èπ◊? ¶μ«í∫´· II 6. 7. äéπ éπ∞«-¨»-©-¢√®Ω’ E®Ωy-£œ«ç-*† ߪ÷vûª™ 80 ´’çC ´uèπ◊h©’, Ææ®√-Ææ-J† äéÌ\-éπ\®Ω’ ®Ω÷. 15.50 °jÆæ-©’ îÁLxç-î√®Ω’. ¢√J™ 60 ´’çC NüΔu-®Ω’n©’ äéÌ\-éπ\®Ω’ ®Ω÷. 16 îÌ°æ¤p† îÁLxç-î√®Ω’. öÃ*çí˚ Æœ•sçC †’çúÕ ´’Jçûª áèπ◊\´ ®Ω’Ææ’´· ´Ææ÷©’ îË-¨»®Ω’. ¢√J™ Ç®Ω’-í∫’®Ω’ (Åçü¿®Ω÷ ´’í∫-¢√Í®) ÊÆ´-èπ◊©’, ¢√J †’çúÕ áô’-´çöÀ ®Ω’Ææ’´· ´Ææ÷©’ îËߪ’-™‰ü¿’. ¢Á·ûªhç •%çü¿ç™ 20] Çúø-¢√®Ω’ ¢√J™ äéπ®Ω’ öÃ*çí˚ Æœ•sçC. °j ü¿û√hç-¨¡-´·†’ äéπ °æöÀd-éπ™  §Òçü¿’-°æ-J* Åçü¿’-™E N’T-L† í∫∞¡x/ë«S-©†’ °æ‹Jç-°æ¤´·. X ´’Jߪ· Y ņ’ †í∫-®Ω-´·-©™ NüΔu-N-≠æ-ߪ’éπ ≤ƒn®· N´-®Ω-´·©’ †í∫®Ωç: X †í∫®Ωç: Y §ÚÆæ’dví¬úø’ußË’ö¸q §ÚÆæ’d ví¬úø’ußË’ö¸q 36° ví¬úø’u-ßË’ö¸q 27% Åçúø®˝ ví¬úø’ußË’ö¸q 34] (a) (b) (c) (d) (e) 8. §ƒ®∏Ω-¨»© ≤ƒn®· 180° ví¬úø’u-ßË’ö¸q 25% §ƒ®∏Ω-¨»© ≤ƒn®· 90° Åçúø®˝ ví¬úø’u-ßË’ö¸q °j *vûª-°æ-ô-´·-†-†’-Ææ-Jç* Ñ Cí∫’´E*a† v°æ¨¡o-©èπ◊ Ææ´÷-üμΔ-†´·©’ É´¤y´·. X †í∫-®Ω-´·™ 70 ´’çC §ÚÆˇd–ví¬úø’u-ßË’ö¸q Öçõ‰, -Ç- †í∫-®Ωç™ NüΔu-®Ω’n© ïØ√¶μ« áçûª? Y †í∫-®Ω-´·™ §ƒ®∏Ω-¨»© ≤ƒn®· NüΔu-®Ω’n© ¨»ûª°æ¤ Ææçêu áçûª? X †í∫-®Ω-´·-™ E ví¬úø’u-ßË’ö¸q ´’Jߪ· Y †í∫-®Ω-´·-™ E ví¬úø’u-ßË’ö¸q E≠æpAh 0.45, Y †í∫-®Ω-´·™E NüΔu-®Ω’n© ïØ√¶μ« áçûª? X †í∫-®Ω´· ´’Jߪ· Y †í∫-®Ω-´·-©†’ éπL°œ ví¬úø’u-ßË’ö¸q ´’Jߪ· §ÚÆˇd–ví¬úø’u-ßË’ö¸q ≤ƒn®· NüΔu-®Ω’n© E≠æpAh áçûª? Y †í∫-®Ω-´·™ à ≤ƒn®· NüΔu-®Ω’n©’ ûªèπ◊\´? ÉçúÕ-ߪ÷™ Æœ¢Á’çö¸ NE-ßÁ÷-í∫´· (N’L-ߪ’Ø˛ ô†’o-©™) 55 45 45 30 25 15 25 20 Öûªh®Ω v§ƒçûª´· ü¿éÀ~ù v§ƒçûª´· 2001 2002 °æPa´’ v§ƒçûª´· ûª÷®Ω’p v§ƒçûª´· Ñ Cí∫’´ v°æ¨¡o© π◊ °j *vûª-°æ-ô-´·-†-†’-Ææ-Jç* Ææ´÷-üμΔ-†´· É´¤y´·. 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