Data Interpretation for IBPS Clerk Mains | Syndicate PO: Set- 41

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 Data Interpretation for IBPS Clerk Mains | Syndicate PO

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Data Interpretation for IBPS Clerk Mains: Set- 41


Directions:(1-5) Study the following information carefully and answer the questions. The following table gives the variation in the productivity of various processes of production.The data relates to two cases where one of the two variables involved (i.e. labour) is varied while the other (i.e. capital) is kept constant.

Variable Labour Variable Labour
Amount of Capital (C) Number of Labourers (L) Average Output (Q/L) Amount of Capital (C) Number of Labourers (L) Average Output (Q/L)
10 0 0 20 0 0
10 1 30 20 1 50
10 2 45 20 2 60
10 3 50 20 3 70
10 4 50 20 4 74
10 5 48 20 5 76
10 6 46 20 6 73
10 7 40 20 7 64
10 8 35 20 8 56
10 9 30 20 9 48
10 10 25 20 10 41

Capital and Labour are the only two variables involved in the production process.          Total output = Q , Average output = Q/L (i) Marginal output, when the number of labourers employed is n = total output when the number of labourers employed is n– total output when the number of labourers is (n – 1) units.

1.What will be the marginal output when 10 units of capital is invested and 6 labourers are employed?
a. 36
b. 40
c. 44
d. 48
e. None of the Above

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A. 36

First of all, the data has to be tabulated column wise with variables, capital, labour, average output, total output and marginal output:

At 10 units Capital At 20 Units Capital
No. of Labourers (L) Average Output (Q/L) Total Output (Q) Marginal Output No. of Labourers (L) Average Output (Q/L) Total Output (Q) Marginal Output
0 0 0 0 0 0
1 30 30 30 1 50 50 50
2 45 90 60 2 60 120 70
3 50 150 60 3 70 210 90
4 50 200 50 4 74 296 86
5 48 240 40 5 76 380 84
6 46 276 36 6 73 438 58
7 40 280 4 7 64 448 10
8 35 280 0 8 56 448 0
9 30 270 -10 9 48 432 -16
10 25 250 -20 10 41 410 -22

As per the solution (table) when 10 units of capital and six labourers are employed, the marginal output is 36 units.

2.When x labourers are employed investing 10 units of capital, the total output is ‘a’ units. The corresponding total output for an investment of 20 units of capital is ‘b’ units. In how many of the given instances is b > 3a/2?
a. 5
b. 6
c. 7
d. 8
e. 9

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C. 7

First of all, the data has to be tabulated column wise with variables, capital, labour, average output, total output and marginal output:

At 10 units Capital At 20 Units Capital
No. of Labourers (L) Average Output (Q/L) Total Output (Q) Marginal Output No. of Labourers (L) Average Output (Q/L) Total Output (Q) Marginal Output
0 0 0 0 0 0
1 30 30 30 1 50 50 50
2 45 90 60 2 60 120 70
3 50 150 60 3 70 210 90
4 50 200 50 4 74 296 86
5 48 240 40 5 76 380 84
6 46 276 36 6 73 438 58
7 40 280 4 7 64 448 10
8 35 280 0 8 56 448 0
9 30 270 -10 9 48 432 -16
10 25 250 -20 10 41 410 -22

When 1 unit of labour is employed, a = 30 and b = 50

b > (1.5) a

Verifying in this way, we find that, b > (1.5) a for x = 1, 5, 6, 7, 8, 9 and 10

There are six such instances.

3.When a capital of 10 units is invested, how many labourers should be employed in the process for which the marginal output is zero?
a. 5
b. 6
c. 7
d. 8
e. 9

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D. 8

First of all, the data has to be tabulated column wise with variables, capital, labour, average output, total output and marginal output:

At 10 units Capital At 20 Units Capital
No. of Labourers (L) Average Output (Q/L) Total Output (Q) Marginal Output No. of Labourers (L) Average Output (Q/L) Total Output (Q) Marginal Output
0 0 0 0 0 0
1 30 30 30 1 50 50 50
2 45 90 60 2 60 120 70
3 50 150 60 3 70 210 90
4 50 200 50 4 74 296 86
5 48 240 40 5 76 380 84
6 46 276 36 6 73 438 58
7 40 280 4 7 64 448 10
8 35 280 0 8 56 448 0
9 30 270 -10 9 48 432 -16
10 25 250 -20 10 41 410 -22

As per the table (solutions) marginal output is zero, for a capital of 10 units, when 8 units of labour was engaged.


4.What is the magnitude of difference between the marginal output when, a capital of 10 units and number of labourers employed is 3, is engaged and when, a capital of 20 units and number of labourers is 9, is engaged?
a. 44
b. 68
c. 76
d. 74
e. 82

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C. 76

First of all, the data has to be tabulated column wise with variables, capital, labour, average output, total output and marginal output:

At 10 units Capital At 20 Units Capital
No. of Labourers (L) Average Output (Q/L) Total Output (Q) Marginal Output No. of Labourers (L) Average Output (Q/L) Total Output (Q) Marginal Output
0 0 0 0 0 0
1 30 30 30 1 50 50 50
2 45 90 60 2 60 120 70
3 50 150 60 3 70 210 90
4 50 200 50 4 74 296 86
5 48 240 40 5 76 380 84
6 46 276 36 6 73 438 58
7 40 280 4 7 64 448 10
8 35 280 0 8 56 448 0
9 30 270 -10 9 48 432 -16
10 25 250 -20 10 41 410 -22

From the data given in the table above we get,

In the first case, when a capital of 10 units and labour of 3 units is engaged then the marginal output is 60.

In the second case, when a capital of 20 units and labour of 9 units is engaged then the marginal output is -16.

Therefore, the magnitude of difference = 60 – (-16) = 76.

 

5.What is the average of marginal output when, in first case, 10 units of capital is invested and seven units of labour is employed and in another case 20 units of capital is invested and 5 units of labour is employed?
a. 54
b. 44
c. 34
d. 24
e. 14

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B. 44

First of all, the data has to be tabulated column wise with variables, capital, labour, average output, total output and marginal output:

At 10 units Capital At 20 Units Capital
No. of Labourers (L) Average Output (Q/L) Total Output (Q) Marginal Output No. of Labourers (L) Average Output (Q/L) Total Output (Q) Marginal Output
0 0 0 0 0 0
1 30 30 30 1 50 50 50
2 45 90 60 2 60 120 70
3 50 150 60 3 70 210 90
4 50 200 50 4 74 296 86
5 48 240 40 5 76 380 84
6 46 276 36 6 73 438 58
7 40 280 4 7 64 448 10
8 35 280 0 8 56 448 0
9 30 270 -10 9 48 432 -16
10 25 250 -20 10 41 410 -22

Marginal output in first case of 10 units of capital is invested and seven labourers is employed = 4

Marginal output in another case of 20 units of capital is invested and five labourers is employed = 84

Average of marginal output = (4+84)/2 = 44

Directions:(6-10) Refer to the following table and remove the questions.           The following table gives the number of topics authored or co-authored by Kavita and her six friends. For example, Kavita alone authored 6 topics while she coauthored 18 topics with Neha, 10 topics with Noopur and likewise. The distribution of topics and distribution of total number of books are shown in Pie charts.

6.If all the topics which are authored individually by any person are of physical sciences, then approximately what percentage (approx) of the number of topics of physical sciences are co-authored by two persons?
a. 53%
b. 54%
c. 47%
d. 42%
e. 35%

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C. 47%

No. of topics authored individually = 6 + 7 + 4 + 3 + 2 + 4 = 26

Total number of topics of physical sciences = 35% of (140) = 49

Number of topics of physical sciences co-authored by two persons = 49 – 26 = 23 Percentage of topics of physical sciences co-authored by two persons = (23/49 * 100) = 46.94% ~ 47%

7.What is the total number of topics, which are authored or co-authored by either Sarita or Sweta?
a. 21
b. 28
c. 77
d. 63
e. 70

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D. 63

Topics authored or co-authored by either Sarita or Sweta are:

Sweta + Sarita – (Sweta and Sarita)

(7 +8+ 7+ 13+3) + (8 + 7 +7+ 3+7) – 7= 63

8.All the topics on Social Science have been authored individually or co-authored by Sweta. If, Sweta has expertise only on Social Science and Arts, then find out the percentage of topics co-authored by Sweta on Arts out of the total number of topics on Arts?
a. 52.65%
b. 36.89%
c. 72.28%
d. 48.57%
e. None of these

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D. 48.57%

Total number of topics of Social Science = .15*140 = 21

So according to question, all the 21 topics have been authored individually or co-authored by Sweta.

Number of topics authored individually by Sweta = 0

Number of topics co-authored by Sweta = 38

So, the number of topics co-authored by Sweta on Arts = 38 – 21 = 17

Total number of topics on Arts = .25*140 = 35

Therefore, the percentage of topics co-authored by Sweta on Arts out of the total number of topics on Arts: = 17*100/35 = 48.57%

9.For which person is the difference between, the number of topics authored individually by that person and the total number of topics co-authored by that person with someone, maximum?
a. Shweta
b. Noopur
c. Neha
d. Priya
e. Both (a) and (c)

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E. Both (a) and (c)

  Topics authored alone Topics co-authored with other person Difference
Kavita 6 32 26
Neha 7 45 38
Noopur 4 36 32
Sweta 0 38 38
Sarita 3 29 26
Saumya 2 23 21
Priya 4 25 21

From table we conclude that maximum difference is for Neha and Sweta i.e. 38

10.What is the difference between total number of topics co-authored by two persons and the total number of topics which are authored individually?
a. 98
b. 102
c. 88
d. 104
e. 96

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C. 88

Given, Total number of topics = 140

Total number of topics authored individually = 6+7+4+3+2+4 = 26

Therefore, Total number of topics co-authored by two persons = 140 – 26 = 114 Required difference = 114 – 26 = 88


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