how to solve this

Question

An Institute having 450 employees has sent all its employees for training in one or more areas out of HRM,Computer Skills and Financial Skills. The employees are classified into two categories — Officers and Clerks, who are in the ratio of 4 : 5. 10% of the Officers take training only in Computer skills, 16% of the Clerks take training only in HRM which is equal to the number of Officers taking training only in Financial Skills and 50 % of the number of Officers taking training in HRM and Financial Skills both. 6% of the total employees take training in all the three, of which two-thirds are officers. 10%of the total employees take training in HRM and Computer Skills both, which is five times the number of Clerks taking training in Computer Skills and Financial Skills. 10% of the Clerks take training in HRM and Computer Skills both. The number of officers taking training only in HRM is 25 % of the number of Clerks taking training only in HRM.20 % of the total number of employees take training only in Computer Skills. Number of clerks taking training in HRM and Financial skills both is 20 % of the total number of Clerks.

106. Total how many officers take training in HRM ?
1)110  2)128   3)118   4)98   5) None of these

107. Total how many Clerks take training in Computer Skills but not in HRM ?
1)113  2)104   3)88  4)79  5) None of these

108. Total how many employee s take training in Financial Skills but not in HRM?
1)106  2)135  3)127  4)134   5) None of these

109. Total how many Clerks take training in Financial Skills?
1)115  2)106  3)47  4)97  5) None of these

110. What per cent of the total number of Officers take training in Computer Skills but not in Financial Skills?
1)25  2)40  3)20   4)15   5) None of these

Answer 1

#Officers $=\frac{4}{4+5}\times 450 = 200$

#Clerks $= 450 -200 = 250$

All the non-highlates data in below table are just taken from the given passage. The highlated ones are derived using set formula and the bold and highlated ones derived in the second step.

number of Officers taking training in HRM and Financial Skills both

Does this include the officers taking training in all three? AFAIK it should, but by doing so I'm not getting any answer in choice. So, for now assuming this is exclusively for GRM + FS and not CS. Similarly for all the "both" cases in passage.

 

	Officers	Clerks	Total
Total	200	250	450
HRM only	10	40	50
CS only	20	70	90
FS only	40	47	87
HRM+CS	20	25	45
CS+FS	12	9	21
HRM+FS	80	50	130
HRM+CS+FS	18	9	27

 

106. Officers in HRM = HRM only + (HRM + CS) + (HRM + FS) + (HRM + CS + FS)

$ = 10 + 20 + 80 + 18 = 128$.

107. Clerks in CS but not in HRM = CS only + (CS + FS) $= 70 + 9 = 79.$

108. Employees in FS but not in HRM = FS only + (FS + CS) $=87+21 = 108.$

109. Clerks in FS = FS only + (FS + HRM) + (FS + CS) + (FS + CS + HRM) $=47 + 50 + 9 + 9 = 115.$

110. Officers in CS but not in FS = CS only + (CS + HRM) $= 20 + 20 = 40.$ So, $\frac{40}{200} \times 100\% = 20\%.$

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Considering both case as non-excluisve as it should be:

	Officers	Clerks	Total
Total	200	250	450
HRM only	10	40	50
CS only	20	70	90
FS only	40	74	114
HRM+CS	20	25	45
CS+FS	66	9	75
HRM+FS	80	50	130
HRM+CS+FS	18	9	27

 

106. Officers in HRM = HRM only + (HRM + CS) + (HRM + FS) - (HRM + CS + FS)

$ = 10 + 20 + 80 - 18 = 92$.

107. Clerks in CS but not in HRM = CS only + (CS + FS) - (CS + FS + HRM) $= 70 + 9 - 9 = 70.$

108. Employees in FS but not in HRM = FS only + (FS + CS) - (FS + CS + HRM) $=114+75-27 = 162.$

109. Clerks in FS = FS only + (FS + HRM) + (FS + CS) - (FS + CS + HRM) $=74 + 50 + 9 - 9 = 124.$

110. Officers in CS but not in FS = CS only + (CS + HRM) - (CS + HRM + FS) $= 20 + 20 -18= 22.$ So, $\frac{22}{200} \times 100\% = 11.1\%.$

 

Comments

How those derived data are calculated?