#DILR-26

A survey was done in a city by an independent body to check the popularity of the bikes - Hero, Honda, Bajaj, Suzuki, TVS and KTM. Total 6300 people participated in the survey. Each person likes at least one of the six bikes. Further, we know the following:-

(i)The number of persons who like exactly one bike to the number of persons who like exactly two bikes to the number of persons who like exactly three bikes to the number of persons who likes exactly four bikes is in the ratio 4:3:2:1, respectively.
(ii)The persons who like TVS, like neither Hero nor Suzuki.
(iii)The persons who like Honda, like neither KTM nor TVS.
(iv)The persons who like KTM, like neither Hero nor TVS.
(v)The number of persons who like only one bike is equal for each bike.
(vi)The number of persons who like exactly two bikes is equal for each possible combination of only two liked bikes. Similarly, the number of persons who like exactly three bikes is equal for each for each possible combination of only three liked bikes.

1)How many persons like Suzuki but does not like Bajaj?
(i)1302
(ii)1360
(iii)1435
(iv)1365

2)How many persons like only Hero and Bajaj together?
(i)189
(ii)378
(iii)210
(iv)Cannot be determined

3)How many persons does not like KTM?
(i)1092
(ii)2342
(iii)4598
(iv)5208

4)How many persons like exactly three bikes but do not like KTM?
(i)990
(ii)1008
(iii)1260
(iv)1386

SOLUTION-


1)Number of people like Suzuki but not Bajaj = Only Suzuki + (Suzuki + one other bike except Bajaj) + (Suzuki + exactly 2 other bikes except Bajaj) + (Suzuki + exactly 3 other bikes except Bajaj)
= 420 + 3*210[(Suzuki+Honda)+(Suzuki+Hero)+(Suzuki+KTM)] + 252(Honda+Hero+Bajaj)
=420 + 630 + 252 = 1302 ANS

2) Only Hero and Bajaj = ex2/9 = 1890/9 = 210 ANS

3)Persons do not like KTM = Total - Likes KTM
                                                   = 6300 - (420 + 2*210 + 252)
                                                   = 5208 ANS

4) Total combinations for ex3 bikes = 5
Out of these 5 possibilities, 1 combination has KTM(KTM + Bajaj + Suzuki)
Total number of people = 4*ex3  = 4*252 = 1008 ANS
                                        














Comments

  1. Unknown10 March 2019 at 23:26

    Pls explain the table!!

    ReplyDelete
    Replies
    1. Quantose11 March 2019 at 00:14

      The table follows same concept used in Games and Tournament when a team plays matches with other teams.
      So if we see the first row,the person who likes TVS does not like Honda,KTM,Hero or Suzuki
      So the person liking TVS is left with two option-
      1)He likes only TVS
      2)He likes both(TVS and Bajaj)
      Similarly for Honda we have checked combination of Honda with TVS in row 1,so we will be checking for other possibilities
      The person liking Honda likes Hero,Bajaj and Suzuki
      Now this man can like only Honda,Honda+1 other bike,Honda + 2 other bikes or Honda + 3 other bikes
      Same goes for other combinations.
      Now for the values of ex2,2x3,ex4 and ex5
      For a person to like exactly 2 bikes one of which should be Honda,we has 3 options-Hero,Bajaj or Suzuki ,i.e, 3 cases for ex2
      For exactly3-out of Hero,Bajaj and Suzuki,we can select any 2 bikes and the third one should be Honda,i.e,Hero-Bajaj,Hero-Suzuki or Bajaj-Suzuki
      For ex4-we have only 1 case when we select all the 4 bikes

      Hope this helps:)

      Delete

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