Q(6 – 10). Study the following bar chart carefully and answer the questions given beside.
The graph given below represents the number of male employees (in lakhs) and the number of female employees (in lakhs) in each of seven organizations viz. ECIL, BHEL, CCE, HCL, SAIL, DRDO and NCL in various Government offices in India.
The males and females in any subsidiary comprise the total workforce of that subsidiary and the total workforce population of the seven subsidiaries together is equal to the one fourth population of the country.
6. For how many subsidiaries is the percentage of population of that subsidiary less than 14.5% of the one by fourth part of the country’s population?
(a) Zero
(b) One
(c) Three
(d) Four
(e) Five
Solution: (d)
The populations (in lakhs) of the subsidiary are tabulated below.
Subsidiary name
Populations (in lakhs)
ECIL
(26.5 + 32.5) = 59.0
BHEL
(25.1 + 20.5) = 45.6
CCE
(32.5 + 30.2) = 62.7
HCL
(38.5 + 32.8) = 71.3
SAIL
(24.5 + 31.2) = 55.7
DRDO
(38.7 + 24.9) = 63.6
NCL
(36.4 + 23.7) = 60.1
Total
418
The total population of the one by fourth part of the country = 418 lakhs
14.5% of the one by fourth part of the country’s populations = (0.145 \(\displaystyle \times \) 418) = 60.61 lakhs
The subsidiary which have less than 14.5% of the one by fourth part of the country’s population, i.e., which have less than 60.61 lakhs are ECIL, BHEL, SAIL and NCL.
Hence, number of subsidiary = 4
7. For how many subsidiaries is the ratio of the number of females to the number of males less than that for the one by fourth part of the country?
(a) 1
(b) 2
(c) 3
(d) 4
(e) 5
Solution: (d)
Subsidiary name
Number of males (in lakhs)
Number of females (in lakhs)
Number of females : Number of males
ECIL
26.5
32.5
1.22
BHEL
25.1
20.5
0.81
CCE
32.5
30.2
0.92
HCL
38.5
32.8
0.85
SAIL
24.5
31.2
1.27
DRDO
38.7
24.9
0.64
NCL
36.4
23.7
0.65
Total
222.2
195.8
0.88
The total number of males in the one by fourth part of the country = 222.2 lakhs
The total number of females in the one by fourth part of the country = 195.8 lakhs
Ratio of the number of females in the one by fourth part of the country to that of males = 0.88
We can observe from the table that for ECIL and SAIL, the ratio is greater than 1
For CCE, the ratio is 0.92, which is greater than the required ratio.
For all the other subsidiary viz. BHEL, HCL, DRDO and NCL, the ratio is less than 0.88
Hence number of subsidiary which has less than the ratio of the number of females to the number of males are four
8. If, in each subsidiary, exactly 60% of the males and 40% of the females are literate, which subsidiary has the third highest illiterate population?
(a) ECIL
(b) DRDO
(c) HCL
(d) CCEE
(e) NCl
Solution: (b)
Number of illiterates in subsidiary ECIL = (0.4 \(\displaystyle \times \) 26.5 + 0.6 \(\displaystyle \times \) 32.5) = 30.1
Number of illiterates in subsidiary BHEL = (0.4 \(\displaystyle \times \) 25.1 + 0.6 \(\displaystyle \times \) 20.5) = 22.34
Number of illiterates in subsidiary CCE = (0.4 \(\displaystyle \times \) 32.5 + 0.6 \(\displaystyle \times \) 30.2) = 31.12
Number of illiterates in subsidiary HCL = (0.4 \(\displaystyle \times \) 38.5 + 0.6 \(\displaystyle \times \) 38.8) = 35.08
Number of illiterates in subsidiary SAIL = (0.4 \(\displaystyle \times \) 24.5 + 0.6 \(\displaystyle \times \) 31.2) = 28.52
Number of illiterates in subsidiary DRDO = (0.4 \(\displaystyle \times \) 38.7 + 0.6 \(\displaystyle \times \) 24.9) = 30.42
Number of illiterates in subsidiary NCL = (0.4 \(\displaystyle \times \) 36.4 + 0.6 \(\displaystyle \times \) 23.7) = 28.78
Hence, the third highest number of illiterates are in DRDO
9. If it is given that that there are no widows or widowers in the seven subsidiary then, For how many subsidiary is it possible that the population of the unmarried persons in the subsidiary is less than 10% of the population of the subsidiary?
(a) One
(b) Two
(c) Three
(d) Four
(e) Six
Solution: (d)
In Subsidiary ECIL, since there are 26.5 lakhs males and 32.5 lakhs females, there can be a maximum of 26.5 lakhs married couples, a total of (26.5 \(\displaystyle \times \) 2) = 53 lakhs married persons. Hence, the remaining (32.5 – 26.5) = 6 lakhs persons will be unmarried. This is the minimum number of persons who will be unmarried.
Now,
Subsidiary name
Number of males (in lakhs)
Number of females (in lakhs)
Minimum Number of unmarried person
10% population of the subsidiary
ECIL
26.5
32.5
6.0
5.90
BHEL
25.1
20.5
4.6
4.56
CCE
32.5
30.2
2.3
6.27
HCL
38.5
32.8
5.7
7.13
SAIL
24.5
31.2
6.7
5.57
DRDO
38.7
24.9
13.8
6.36
NCL
36.4
23.7
12.7
6.01
Total
222.2
195.8
26.4
41.8
Comparing the Minimum Number of unmarried persons with 10% population of the subsidiary of each subsidiary, we can conclude that only in subsidiary CCE and subsidiary HCL has the number of unmarried persons are less than that of 10% of the population of the subsidiary.
10. For which subsidiary/subsidiary is the number of males as a percentage of the total number of males out of one fourth population of the country less than 13.25%?
(a) ECIL, DRDO and BHEL
(b) BHEL only
(c) HCL and SAIL
(d) BHEL, SAIL, ECIL and NCL
(e) ECIL, BHEL and SAIL
Solution: (e)
Total number of males in the one fourth part of the country = 222.2 lakhs
13.25% of total number of males in one fourth population of the country
