Group QuestionAnswer the following question based on the information g...
First identify how the data is to be presented.
Each employee travels by one of four modes of transport - Metro train (M), Local train (L), office bus (B) and own vehicle (V)
Also, the employees are classified as males and females as well as technical or non-technical.
Hence, the entire classification can be as shown below.
Denote employees by acronyms
i.e. Male = M, Female = F, Technical = T and Non-Technical = N
Classify each type of employee as gender-employee-type-(mode of transport)
e.g. a male technical employee travelling by local train or Metro train is MT(L) or MT(M) respectively and a female non-technical employee travelling by office bus is FN(B), and so on. Similarly, male technical employees are MT and total female employees travelling by Metro train are F(M) and so on.
Now, total employees = 2100 such that males and females are in the ratio 19 : 16
Number of males = (19/35) * 2100 = 1140 and number of females = 2100- 1140 = 960
Some information is directly given.
Of all the male employees who use the office bus, 123 are non-technical staff i.e. MN(B) = 123
Also, FN(M) = 136
Fill up the data obtained so far in the table.
Now, consider the direct information given for each type of vehicle.
Own Vehicle (V)
14% of employees use their own vehicle.
(V) = 0.14x2100 = 294
The ratio of technical to non-technical staff using their own vehicle is 2 :1 T(V) = (2/3) x 294 = 196 and N(V) = 294 - 196 = 98
Now, FT(V) = (1/3) x MT(V) and FT(V) = MN(V)
Now FT(V) + MT(V) = T(V)
FT(V) + 3FT(V) = 196
FT(V) = 49
MT(V) = 3 x 49 = 197 and MN(V) = 49 Now, MN(V) + FN(V) = N(V) = 98
FN(V) = 98 - 49 = 49
After the number of people using their own vehicle is removed, one-third of the remaining employees use the Metro trains.
(M) = (2100- 294)/3 = 602
Also (L) = 3(B)
(L) + (B) = 2100 - [(M) + (V)]
(L) + (B) = 2100 - 602 - 294 = 1204
Solving the two equations for (L) and (B), (B) = 301 and (L) = 903
Consider Local Train (L)
FN(L) = 20% of F and FN(L) = 80% of FT(L)
FN(L) = 0.2 x 960 = 192 and FT(L) = 192/0.8 = 240
F(L) = FN(L) + FT(L) = 192 + 240 = 432
M(L) = (L) - F(L) = 903 - 432 = 471
M(L) = MT(L) + MN(L) = 471
Also, MT(L) - MN(L) = 11
Solving these two equations, MT(L) = 241 and MN(L) = 230
T(L) = MT(L) + FT(L) = 241 + 240 = 441 and N(L) = MN(L) + FN(L) = 230 + 192 = 422
Hence, the table becomes:
Now consider Office Bus (B)
MN(B) = 123
FN(B) = (1/7) x (B) and M T (B ): FT(B) = 5 : 4
FN(B) = 301/7 = 43
N(B) = MN(B) + FN(B) = 123 + 43 = 166
T(B) = (B) - N(B) = 301 - 166 = 135
T(B) = MT(B) + FT(B) = 135 and M T (B ): FT(B) = 5 : 4
Solving these two equations, MT(B) = 75 and FT(B) = 60
M(B) = MT(B) + MN(B) = 75 + 123 = 198 and F(B) = 301 - 198 = 103
Now, MT + MN = M = 1140
and MN - MT = 4
MN = 572 and MT = 568
Thus, the table becomes:
Now, observe that the remaining values can be directly filled by addition or subtraction in respective rows or columns.
Hence, the final table is:
Male technical staff that travel by trains = MT(M) + MT(L) = 105 + 241 = 346 Female non-technical staff that do not travel by Local trains = FN(M) + FN(B) + FN(V) = 136 + 43 + 49 = 228
Required difference = 346 - 228 = 118 Hence, option 2.