APTITUDE

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Oddmanout and Series
Data Interpretation
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BACK

PERCENTAGES


EXAMPLE PROBLEMS:

             
13. Difference of two numbers is 1660.If 7.5 % of one number is 12.5% of the other number. Find two numbers?
          SOLUTION:
                     Let the two numbers be x and y.
                      7.5% of x=12.5% of y
                      So 75x=125 y
                           3x=5y
                           x=5/3y.
                    Now x-y=1660
                            5/3y-y=1660
                             2/3y=1660
                                  y=2490
                             So x= 2490+1660
                                     =4150.
                  So the numbers are 4150 , 1660.

14. In expressing a length 81.472 KM as nearly as possible with 3 significant digits ,Find the % error?
             SOLUTION:
                      Error= 81.5-81.472=0.028
             So the required percentage = 0.028/81.472*100%
                                                        = 0.034%

15. In an election  between two persons ,75% of the voters cast their votes out of which 2% are invalid. A got 9261 which 75% of the total valid votes. Find total number of votes?
               SOLUTION:
                             Let x be the total votes.
                             valid votes are 98% of 75% of x.
                             So 75%(98%(75% of x))) = 9261
                              ==>  75/100 *98 /100 * 75 100 *x = 9261
                                      x= 1029 * 4 *100 *4 / 9
                                        = 16800                        
                             So total no of votes =  16800

16 . A's maths test had 75 problems i.e 10 arithmetic, 30 algebra and 35   
       geometry problems. Although  he answered 70% of arithmetic , 40% 
       of algebra and 60 % of geometry problems correctly he didn't pass the 
       test because he got less than 60% of the problems right. How many 
       more questions he would have needed to answer correctly to get a 
       60% passing grade.
             
   SOLUTION:
                 70% of 10 =70/100 * 10
                                                 =7
                  40% of 30 =  40 / 100 * 30 
                                                  = 12
                                 60 % of 35 = 60 / 100 *35 
                                                   = 21
                                So correctly attempted questions = 7 + 12 + 21
                                                                                     =40.
                               Questions to be answered correctly for 60% grade 
                                                                       =60% of 75                    
                                                                       = 60/100 *75
                                                                       =45.
                               So required questions=45-40 = 5

17 . If 50% of (x – y) = 30% of (x + y) then what percent of x is y ?
                         SOLUTION: 
                                        50/100(x-y) =30/100(x+y)
                                        ½ (x-y)= 3/10(x+y)
                                         5x-5y=3x+3y
                                             x=4y
                                      So Required percentage =y/x*100 %
                                                                             =y/4y *100 %
                                                                             = 25%.

18 . If the price of tea is increased by 20% ,find how much percent must a  
       householder reduce her consumption of tea so as not to increase the 
       expenditure?
                     SOLUTION:
                                      Reduction in consumption= R/(100+R) *100%                                 
                                                                         =20/120 *100
                                                                         = 16 2/3 %

19.The population of a town is 176400 . If it increases at the rate of 5%
per annum ,what will be the population 2 years hence? What was it 2 years ago?
                  SOLUTION:
                             Population After 2 years = 176400[1+5/100]2
                                                                      =176400 * 21/20 *21/20
                                            =194481
                 Population 2 years ago = 176400/(1+5/100)2
                                                       = 176400 * 20/21 *20/ 21
                                                       =160000

20.1 liter of water is add to 5 liters of a 20 % solution of alcohol in water . 
 Find the strength of alcohol in new solution?
                      SOLUTION:
                                Alcohol in 5 liters = 20% of 5
                                                              =1 liter
                                Alcohol in 6 liters of new mixture = 1liter
                                So % of alcohol is =1/6 *100=16 2/3%

21. If A earns 33 1/3  more than B .Then B earns less than A by what   
 percent?
                SOLUTION:
                        33 1/3 =100 / 3
                        Required Percentage = (100/3)/(100 + (100/3)) *100 %
                                                          = 100/400 *100 = 25 %