College Math

College Math Study Guide

5.12 Chapter 5: Answers 1. (i) d, (ii) a, (iii) b Solution: (i) The total commission would be (11.7+16.25+20.8+18.2+24.7) 91.65. The total bonus would be (1.5+16.25+20.8+18.2+1.98)58.73. The desired percentage would be 91.65/58.73*100 = 156.05%. (ii) The total expenditure in 2010 would be (144+49+1.5+11.7+41.5) 247.7 while total expenditure in 2014 would be (210+71+1.98+24.7+49) 356.68. The desired percentage would be 247.7/356.68*100 = 69.45%. (iii) The total expenditure for 2014 would be (210+71+1.98+24.7+49) 356.68 while the total expenditure would be (168+66.5+18.2+18.2+44) 314.9. The percentage increase in total expenditure would be (356.68-314.9)/314.9*100 = 13.27%. 2. (i) c, (ii) a Solution: (i) The average reserves would be {(1320+1860+1260+1680+1560+2160+2520+1560)/8= 1740. The years in which the reserves are above average are 2007-08, 2011-12, 2012-13, that is 3 years, while the reserves are below average in 2006-07, 2008-09, 2009-10, 2010-11, 2013-14, that is 5 years. The desired ratio would be 3:5 (ii) Let us first see whether all the options show the increase in reserves with respect to previous years or not. It can be observed that the year 2010-11 witnesses a fall in reserves with respect to the previous year, hence, we exclude that option. Let us check for other options now. The percentage increase for the rest of the three options would be calculated as follows: 2007-08 = (1860-1320)/1320*100 = 40.91% 2009-10= (1680- 1260)/1260*100 = 33.33% 2011-12= (2160-1560)/1560*100 = 38.46% Hence, the highest increase is achieved in 2007-08. 3. a Solution: Range = Highest number – lowest number In this case, highest number in the series = 97 and lowest number = 45. Hence, range = 97-45 = 52

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